MikaStars39/nano-eval huggingface dataset:
1 mol of butanediol and 1 mol of adipic acid are used to synthesize a polyester where $\overline{{{{M_{\mathrm{n}}}}}} = 5000$. The amounts of the two difunctional substances are exactly the same, and the effect of the end groups on $\overline{{{M_{\mathrm{n}}}}}$ is ignored. Determine the degree of reaction $p$ at which the polycondensation reaction ends.

Options:
A. 0.92
B. 0.84
C. 0.90
D. 0.95
E. 0.88
F. 0.89
G. 0.87
H. 0.91
I. 0.98
J. 0.93
Answer: I
Calculate the mixing entropy of 100 mL of a styrene-xylene solution with a concentration of 0.01 mol·L at 20 °C is().The density of xylene at 20 °C is $0.861 \mathrm{g \cdot cm^{-3}}$.

Options:
A. $$
0. 1 0 5 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
B. $$
0. 0 0 9 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
C. $$
0. 0 7 1 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
D. $$
0. 2 4 5 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
E. $$
0. 1 3 7 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
F. $$
0. 0 5 2 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
G. $$
0. 0 6 4 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
H. $$
0. 0 3 6 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
I. $$
0. 0 8 3 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
J. $$
0. 0 9 8 \ ( \mathrm{J} \cdot\mathrm{K}^{-1} )
$$
Answer: G
The sedimentation coefficient $S$ and diffusion coefficient $D$ of hemoglobin in water, corrected to the values ​​at $293 \mathrm{~K}$, are $4.41 \times 10^{-13} \, \mathrm{s}$ and $6.3 \times 10^{-7} \, \mathrm{m^{2} \cdot s^{-1}}$respectively. At $293 \mathrm{~K}$, the specific volume is $0.749 \times 10^{-3} \, \mathrm{m}^{3} \cdot \mathrm{kg}^{-1}$, and the density of water is $998 \times 10^{3} \, \mathrm{kg} \cdot \mathrm{m}^{-3}$. Calculate the relative molecular weight of this hemoglobin?

Options:
A. 6.02
B. 8.33
C. 9.17
D. 5.42
E. 4.95
F. 6.75
G. 7.12
H. 5.84
I. 4.51
J. 7.89
Answer: F
A cross-linked natural rubber sample was weighed and swelled in n-decane solvent at 25°C. When the swelling equilibrium was reached, the volume swelling ratio was measured to be 4.0. Given the polymer-solvent interaction parameter $\chi_{1}=0.42$, the polymer density $\rho_{2}=0.91 \mathrm{g \cdot cm^{-3}}$, and the molar volume of the solvent is 195.86 cm³·mol⁻¹, calculate the shear modulus $G$.$(R=8.31 ​​\mathrm{~J \cdot K^{-1} \cdot mol^{-1}~})$ of the sample?

Options:
A. $$
5 \times1 0^{5} ( \mathrm{P a} )
$$
B. $$
1 \times1 0^{6} ( \mathrm{P a} )
$$
C. $$
2 \times1 0^{5} ( \mathrm{P a} )
$$
D. $$
3 \times1 0^{5} ( \mathrm{P a} )
$$
E. $$
6 \times1 0^{5} ( \mathrm{P a} )
$$
F. $$
8 \times1 0^{5} ( \mathrm{P a} )
$$
G. $$
7 \times1 0^{5} ( \mathrm{P a} )
$$
H. $$
4 \times1 0^{5} ( \mathrm{P a} )
$$
I. $$
1 \times1 0^{5} ( \mathrm{P a} )
$$
J. $$
9 \times1 0^{5} ( \mathrm{P a} )
$$
Answer: I
If it is known that the photocurrent of a silicon photodiode is $50 \mu\mathrm{A}$ and $300 \mu\mathrm{A}$, with both having a dark current of $1 \mu\mathrm{A}$, their open-circuit voltage in volts is ().

Options:
A. 110mV,155mV
B. 99mV,146mV
C. 100mV,145mV
D. 105mV,160mV
E. 104mV,150mV
F. 102mV,148mV
G. 108mV,159mV
H. 108mV,152mV
I. 95mV,147mV
J. 103mV,144mV
Answer: F
Consider a planar dielectric waveguide, where the refractive indices for each layer are $n_{1}=2.21$, $n_{2}=2.1$, and $n_{3}=1$, and the waveguide layer thickness is $d=4.6 \mu m$. If the total internal reflection phase shift is $\frac{3}{2} \pi$, what is the total number of modes that can propagate in the waveguide when the incident light wavelength is $1.31 \mu m$?

Options:
A. 7
B. 6
C. 9
D. 8
E. 4
F. 10
G. 3
H. 11
I. 5
J. 12
Answer: I
After a beam of light travels through the suburbs for 2 km, its intensity becomes $1/3$ of the original. After passing through the city for another 2 km, its intensity becomes $1/50$ of the original. If the initial intensity of the beam is $P=1 \, \text{W}$, and the receiving antenna's aperture is 100 mm, with the beam divergence angle $\theta=0.1 \, \text{mrad}$, what is the received optical power at the terminal and the average attenuation coefficient of the atmosphere in the city?

Options:
A. 0.02W,4.5dB/km
B. 0.03W,4.0dB/km
C. 0.03W,5.9dB/km
D. 0.02W,8.2dB/km
E. 0.01W,5.7dB/km
F. 0.03W,7.0dB/km
G. 0.02W,3.8dB/km
H. 0.01W,7.5dB/km
I. 0.02W,6.1dB/km
J. 0.01W,6.5dB/km
Answer: I
The value of $\left( \frac{1+\sqrt{3} \; \mathrm{i}} {1-\sqrt{3} \; \mathrm{i}} \right)^{10}$ is ().

Options:
A. $$
\frac{1}{2}+\frac{\sqrt{3}}{2} \mathrm{i}
$$
B. $$
-\sqrt{3}+i
$$
C. $$
\frac{1}{2}-\frac{\sqrt{3}}{2} \mathrm{i}
$$
D. $$
\sqrt{3}-1
$$
E. $$
\frac{\sqrt{3}}{2}+\frac{1}{2} \mathrm{i}
$$
F. $$
-\frac{1}{2}-\frac{\sqrt{3}}{2} \mathrm{i}
$$
G. $$
-\frac{1} {2}+\frac{\sqrt{3}} {2} \mathrm{i}
$$
H. $$
\frac{\sqrt{3}}{2}-\frac{1}{2} \mathrm{i}
$$
I. $$
-\frac{\sqrt{3}}{2}+\frac{1}{2} \mathrm{i}
$$
J. $$
1+\sqrt{3} \mathrm{i}
$$
Answer: G
The solution to the equation $\sin z = i \sinh1$ is ()

Options:
A. $$
z \!=\! \left\{\! \! \begin{array} {l} {{{2 n \pi+\mathrm{i} \,,3}}} \\ {{{( 2 n \!+\! 1 ) \pi-\mathrm{i} \,,}}} \\ \end{array} \right. n=0 \,, \pm1 \,, \pm2 \,, \cdots
$$
B. $$
z \!=\! \left\{\! \! \begin{array} {l} {{{2 n \pi\!-\! \mathrm{i} \,,}}} \\ {{{( 2 n \!+\! 1 ) \pi\!+\! \mathrm{i} \,,}}} \\ \end{array} \right. n=0 \,, \pm1 \,, \pm2 \,, \cdots
$$
C. $$
z \!=\! \left\{\! \! \begin{array} {l} {{{3 n \pi+\mathrm{i} \,,}}} \\ {{{( 3 n\!+\!1 ) \pi-\mathrm{i} \,,}}} \\ \end{array} \right. n=0 \,, \pm1 \,, \pm2 \,, \cdots
$$
D. $$
z \!=\! \left\{\! \! \begin{array} {l} {{{2 n \pi+\mathrm{i}+1 \,,}}} \\ {{{( 2 n \!+\! 1 ) \pi-\mathrm{i} 2 \,,}}} \\ \end{array} \right. n=0 \,, \pm1 \,, \pm2 \,, \cdots
$$
E. $$
z \!=\! \left\{\! \! \begin{array} {l} {{{2 n \pi+\mathrm{i} \,,}}} \\ {{{( 2 n\!+\!1 ) \pi-\mathrm{i} \,,2}}} \\ \end{array} \right. n=0 \,, \pm1 \,, \pm2 \,, \cdots
$$
F. $$
z \!=\! \left\{\! \! \begin{array} {l} {{{2 n \pi+2\mathrm{i} \,,}}} \\ {{{( 2 n \!+\! 1 ) \pi+3\mathrm{i} \,,}}} \\ \end{array} \right. n=0 \,, \pm1 \,, \pm2 \,, \cdots
$$
G. $$
z \!=\! \left\{\! \! \begin{array} {l} {{{2 n \pi - \mathrm{i} \,,}}} \\ {{{( 2 n \!+\! 1 ) \pi+\mathrm{i} \,,}}} \\ \end{array} \right. n=0 \,, \pm1 \,, \pm2 \,, \cdots
$$
H. $$
z \!=\! \left\{\! \! \begin{array} {l} {{{2 n \pi\!+\! \mathrm{i} \,,}}} \\ {{{( 2 n \!+\! 1 ) \pi\!+\! \mathrm{i} \,,}}} \\ \end{array} \right. n=0 \,, \pm1 \,, \pm2 \,, \cdots
$$
I. $$
z \!=\! \left\{\! \! \begin{array} {l} {{{4 n \pi+\mathrm{i} \,,}}} \\ {{{( 4 n \!+\! 1 ) \pi-\mathrm{i} \,,}}} \\ \end{array} \right. n=0 \,, \pm1 \,, \pm2 \,, \cdots
$$
J. $$
z \!=\! \left\{\! \! \begin{array} {l} {{{2 n \pi\!+\! \mathrm{i} \,,}}} \\ {{{( 2 n \!+\! 1 ) \pi\!-\! \mathrm{i} \,,}}} \\ \end{array} \right. n=0 \,, \pm1 \,, \pm2 \,, \cdots
$$
Answer: J
What is the value of the integral $\oint_{c} \frac{\operatorname{sin} \frac{\pi}{4} z}{z^{2}-1} \mathrm{d} z$, where $C: \ \big| z+1 \big| = \frac{1}{2}$?

Options:
A. $$
\frac{1}{4} \pi \mathrm{i}
$$
B. $$
-\frac{\pi}{2} \mathrm{i}
$$
C. $$
\pi \mathrm{i}
$$
D. $$
\frac{\pi \mathrm{i}}{2}
$$
E. $$
\frac{\pi}{4} \mathrm{i}
$$
F. $$
\frac{\sqrt{2}}{4} \pi
$$
G. $$
\frac{\sqrt{2}} {2} \pi\mathrm{i}
$$
H. $$
\frac{\pi}{8} \mathrm{i}
$$
I. $$
\sqrt{2} \pi \mathrm{i}
$$
J. $$
\sqrt{2} \mathrm{i}
$$
Answer: G
What is the value of the integral $\oint_{C} \frac{\mathrm{d} z}{(z-1)^{3}(z+1)^{4}}$,where $C$ is the circle centered at $z=1$ with a radius $R < 2$?

Options:
A. $$
{\frac{8} {1 5}} \pi\mathrm{i}
$$
B. $$
{\frac{7} {1 2}} \pi\mathrm{i}
$$
C. $$
{\frac{1} {2}} \pi\mathrm{i}
$$
D. $$
{\frac{9} {4 0}} \pi\mathrm{i}
$$
E. $$
{\frac{4} {1 0}} \pi\mathrm{i}
$$
F. $$
{\frac{6} {1 8}} \pi\mathrm{i}
$$
G. $$
{\frac{3} {8}} \pi\mathrm{i}
$$
H. $$
{\frac{5} {1 6}} \pi\mathrm{i}
$$
I. $$
{\frac{2} {5}} \pi\mathrm{i}
$$
J. $$
{\frac{1 1} {2 2}} \pi\mathrm{i}
$$
Answer: H
What is the radius of convergence for $\sum_{n=0}^{\infty} \ \operatorname{c o s} \left( \ i n \right) z^{n}$?

Options:
A. $$
\pi
$$
B. $$
{\frac{1} {\pi}}
$$
C. $$
{\frac{2} {\mathrm{e}}}
$$
D. $$
{\frac{1} {\mathrm{e}}}
$$
E. $$
\sqrt{2}
$$
F. $$
\mathrm{e}
$$
G. $$
{\frac{1} {2}}
$$
H. $$
{0}
$$
I. $$
\infty
$$
J. $$
\ln(2)
$$
Answer: D
What is the power series expansion of $f(z) = 1/(z-b)$ in terms of $(z-a)$, where $a$ and $b$ are distinct complex constants?

Options:
A. $$
= \frac{-1} {b-a}+\frac{a-z} {\left( \, a-b \, \right)^{2}}-\frac{\left( \, z-a \, \right)^{2}} {\left( \, b-a \, \right)^{3}}+\cdots+\left( \,1 \, \right) \, \cdot\, \frac{\left( \, a-z \, \right)^{n}} {\left( \, a-b \, \right)^{n+1}}+\cdots
$$
B. $$
= \frac{-1} {b+a}+\frac{z-a} {\left( \, a+b \, \right)^{2}}+\frac{\left( \, a+z \, \right)^{2}} {\left( \, b+a \, \right)^{3}}+\cdots-\left( \,-1 \, \right) \, \cdot\, \frac{\left( \, z+a \, \right)^{n}} {\left( \, b+a \, \right)^{n+1}}+\cdots
$$
C. $$
= \frac{-1} {a-b}+\frac{z-b} {\left( \, b-a \, \right)^{2}}-\frac{\left( \, z-b \, \right)^{2}} {\left( \, a-b \, \right)^{3}}+\cdots+\left( \,1 \, \right) \, \cdot\, \frac{\left( \, z-b \, \right)^{n}} {\left( \, a-b \, \right)^{n+1}}+\cdots
$$
D. $$
= \frac{1} {b-a}+\frac{z-a} {\left( \, a-b \, \right)^{2}}+\frac{\left( \, a-z \, \right)^{2}} {\left( \, b-a \, \right)^{3}}+\cdots-\left( \,1 \, \right) \, \cdot\, \frac{\left( \, a-z \, \right)^{n}} {\left( \, a-b \, \right)^{n+1}}+\cdots
$$
E. $$
= \frac{1} {a-b}+\frac{a-z} {\left( \, b-a \, \right)^{2}}+\frac{\left( \, z-b \, \right)^{2}} {\left( \, a-b \, \right)^{3}}+\cdots-\left( \,1 \, \right) \, \cdot\, \frac{\left( \, z-b \, \right)^{n}} {\left( \, a-b \, \right)^{n+1}}+\cdots
$$
F. $$
= \frac{1} {a+b}+\frac{z-a} {\left( \, b-a \, \right)^{2}}-\frac{\left( \, z+b \, \right)^{2}} {\left( \, a-b \, \right)^{3}}+\cdots-\left( \,1 \, \right) \, \cdot\, \frac{\left( \, z+b \, \right)^{n}} {\left( \, b-a \, \right)^{n+1}}+\cdots
$$
G. $$
= \frac{1} {b-a}-\frac{z+a} {\left( \, b+a \, \right)^{2}}-\frac{\left( \, z+a \, \right)^{2}} {\left( \, b+a \, \right)^{3}}+\cdots+\left( \,1 \, \right) \, \cdot\, \frac{\left( \, z+a \, \right)^{n}} {\left( \, b+a \, \right)^{n+1}}+\cdots
$$
H. $$
= \frac{-1} {b-a}-\frac{z-a} {\left( \, b-a \, \right)^{2}}-\frac{\left( \, z-a \, \right)^{2}} {\left( \, b-a \, \right)^{3}}+\cdots+\left( \,-1 \, \right) \, \cdot\, \frac{\left( \, z-a \, \right)^{n}} {\left( \, b-a \, \right)^{n+1}}+\cdots
$$
I. $$
= \frac{-1} {a-b}+\frac{z-b} {\left( \, b-a \, \right)^{2}}+\frac{\left( \, b-z \, \right)^{2}} {\left( \, a-b \, \right)^{3}}+\cdots-\left( \,-1 \, \right) \, \cdot\, \frac{\left( \, b-z \, \right)^{n}} {\left( \, a-b \, \right)^{n+1}}+\cdots
$$
J. $$
= \frac{1} {b-a}-\frac{z-b} {\left( \, a-b \, \right)^{2}}+\frac{\left( \, b-z \, \right)^{2}} {\left( \, b-a \, \right)^{3}}+\cdots-\left( \,1 \, \right) \, \cdot\, \frac{\left( \, b-z \, \right)^{n}} {\left( \, b-a \, \right)^{n+1}}+\cdots
$$
Answer: H
What is the type of finite singularity of the function $f(z) = \sin \frac{1}{z-1}$?

Options:
A. Integral Singularity
B. Discrete Continuity
C. Annular Point Singularity
D. Removable Discontinuity
E. Regular Singularity
F. Transcendental Singularity
G. Intrinsic Singularity
H. Non-removable Singularity
I. Algebraic Singularity
J. Boundary Point Singularity
Answer: G
The residue of the function $f(z) = \tan(z-1) / (z-1)$ at its finite singularity is ().

Options:
A. $3$,$\frac{-3} {\left( \, 1+k \, \right) \pi}$.
B. $-1$,$\frac{-2} {\left( \, k \, \right) \pi}$.
C. $1$,$\frac{3} {\left( \, 3 k+1 \, \right) \pi}$.
D. $0$,$\frac{1} {\left( \, 2 k+1 \, \right) \pi}$.
E. $0$,$\frac{1} {\left( \, 2 k-1 \, \right) \pi}$.
F. $0$,$\frac{-1} {\left( \, 2 k+2 \, \right) \pi}$.
G. $0$,$\frac{-2} {\left( \, 2 k+1 \, \right) \pi}$.
H. $0$,$\frac{2} {\left( \, 4 k+2 \, \right) \pi}$.
I. $0$,$\frac{-2} {\left( \, 2 k \, \right) \pi}$.
J. $2$,$\frac{-1} {\left( \, k+1 \, \right) \pi}$.
Answer: G
What is the sum of the residues of the function $f(z) = \frac{z^{13}}{(z^{2}-1)(z^{8}+1)}$ at all finite singularities in the complex plane?

Options:
A. 5
B. 2
C. 1
D. 6
E. 8
F. -1
G. 4
H. 0
I. 3
J. 7
Answer: C
The value of the integral $\oint_{| z-\mathrm{i} |=1} \frac{2 \cos z}{(\mathrm{e}+\mathrm{e}^{-1})(z-\mathrm{i})^{3}} \mathrm{d} z$ is ().

Options:
A. $$
2\pi
$$
B. $$
-\pi
$$
C. $$
\frac{-\pi}{\mathrm{i}}
$$
D. $$
2\pi\mathrm{i}
$$
E. $$
0
$$
F. $$
-\pi\mathrm{i}
$$
G. $$
\mathrm{i}\pi
$$
H. $$
\pi\mathrm{i}
$$
I. $$
-\mathrm{i}\pi^{2}
$$
J. $$
\frac{\pi}{2}\mathrm{i}
$$
Answer: F
What is the value of $\oint_{\mid z \mid=\frac{5} {2}} \frac{1} {( \, z-3 \, ) \, ( \, z^{5}-1 \, )} \mathrm{d} z$?

Options:
A. $$
\frac{\pi\mathrm{i}} {2 2 2}
$$
B. $$
- \frac{\pi\mathrm{i}} {1 2 1}
$$
C. $$
- \frac{3 \pi} {1 2 1}
$$
D. $$
\frac{\pi\mathrm{i}} {4 2 2}
$$
E. $$
\frac{\pi\mathrm{i}} {1 1}
$$
F. $$
\frac{2\pi} {3 3 1}
$$
G. $$
- \frac{2 \pi\mathrm{i}} {1 2 2}
$$
H. $$
- \frac{\mathrm{i}} {1 2 2}
$$
I. $$
- \frac{\pi\mathrm{i}} {2 4 2}
$$
J. $$
\frac{\pi} {2 1 2}
$$
Answer: B
After operating at a rated power of 500 megawatts for 31 days, a certain reactor was shut down. Assume the radioactive activity of the fission products produced by each fission is $1.08\times10^{-16}t^{-1.2}$ curies, where $t$ is the time after fission, measured in days. What is the number of curies of fission products in the reactor 24 hours after shutdown?

Options:
A. $$
6. 5 5 {\times} 1 0^{9} C i
$$
B. $$
4. 0 1 {\times} 1 0^{7} C i
$$
C. $$
8. 9 3 {\times} 1 0^{8} C i
$$
D. $$
2. 7 6 {\times} 1 0^{9} C i
$$
E. $$
7. 3 4 {\times} 1 0^{8} C i
$$
F. $$
3. 6 2 {\times} 1 0^{8} C i
$$
G. $$
1. 4 5 {\times} 1 0^{7} C i
$$
H. $$
2. 8 9 {\times} 1 0^{7} C i
$$
I. $$
1. 9 1 {\times} 1 0^{8} C i
$$
J. $$
5. 4 7 {\times} 1 0^{9} C i
$$
Answer: F
The known calorific value of standard coal is $Q=29$ megajoules/kg, and the reactor's electrical power is 1000 megawatts. Assuming the power plant's efficiency is 32%, how many uranium-235 nuclei undergo fission per second? How many kilograms of fissile material are consumed in one year of operation? How much fuel would a coal power plant of the same power require over the same period?

Options:
A. $$
1. 2 3 4 5 {\times} 1 0^{1 7},~1602.8\mathrm{kg},~2.6783\times10^{6}\mathrm{t}$$
B. $$
8. 6 5 4 3 {\times} 1 0^{1 8},~1532.9\mathrm{kg},~3.9783\times10^{6}\mathrm{t}$$
C. $$
4. 5 6 7 8 {\times} 1 0^{1 6},~1472.8\mathrm{kg},~3.6983\times10^{6}\mathrm{t}$$
D. $$
3. 4 5 6 7 {\times} 1 0^{1 9},~1425.8\mathrm{kg},~3.1083\times10^{6}\mathrm{t}$$
E. $$
9. 7 6 5 6 {\times} 1 0^{1 9},~1422.8\mathrm{kg},~3.3983\times10^{6}\mathrm{t}$$
F. $$
2. 3 4 5 6 {\times} 1 0^{1 9},~1322.8\mathrm{kg},~4.2983\times10^{6}\mathrm{t}$$
G. $$
5. 6 7 8 9 {\times} 1 0^{1 8},~1499.9\mathrm{kg},~3.7883\times10^{6}\mathrm{t}$$
H. $$
7. 8 9 0 1 {\times} 1 0^{1 7},~1350.8\mathrm{kg},~2.9983\times10^{6}\mathrm{t}$$
I. $$
6. 7 8 9 0 {\times} 1 0^{1 9},~1422.8\mathrm{kg},~4.0083\times10^{6}\mathrm{t}$$
J. $$
8. 9 0 1 2 {\times} 1 0^{1 8},~1505.8\mathrm{kg},~3.5783\times10^{6}\mathrm{t}$$
Answer: E
There are two beams of parallel thermal neutrons traveling in opposite directions striking a $\mathrm{^{235}U}$ thin sheet. Assume the neutron beam intensity incident from the left at a certain point is $10 \ \mathrm{cm}^{-2} \cdot \mathrm{s}^{-1}$. The intensity of the neutron beam incident from the right is $2 \times 10^{12} \ \mathrm{cm}^{-2} \cdot \mathrm{s}^{-1}$. Given $\Sigma_{\mathrm{a}} = 19.2 \times 10^{2} \ \mathrm{m^{-1}}$, what is the absorption rate at that point?

Options:
A. $$
5. 7 6 \times1 0^{1 3} \; \mathrm{c m}^{-3} \cdot\mathrm{s}^{-1}
$$
B. $$
1. 5 8 \times1 0^{1 2} \; \mathrm{c m}^{-3} \cdot\mathrm{s}^{-1}
$$
C. $$
2. 9 3 \times1 0^{1 3} \; \mathrm{c m}^{-3} \cdot\mathrm{s}^{-1}
$$
D. $$
4. 2 7 \times1 0^{1 3} \; \mathrm{c m}^{-3} \cdot\mathrm{s}^{-1}
$$
E. $$
9. 8 6 \times1 0^{1 2} \; \mathrm{c m}^{-3} \cdot\mathrm{s}^{-1}
$$
F. $$
6. 0 9 \times1 0^{1 1} \; \mathrm{c m}^{-3} \cdot\mathrm{s}^{-1}
$$
G. $$
8. 4 5 \times1 0^{1 2} \; \mathrm{c m}^{-3} \cdot\mathrm{s}^{-1}
$$
H. $$
4. 8 4 \times1 0^{1 1} \; \mathrm{c m}^{-3} \cdot\mathrm{s}^{-1}
$$
I. $$
3. 2 1 \times1 0^{1 3} \; \mathrm{c m}^{-3} \cdot\mathrm{s}^{-1}
$$
J. $$
7. 6 9 \times1 0^{1 4} \; \mathrm{c m}^{-3} \cdot\mathrm{s}^{-1}
$$
Answer: A
A parallel neutron beam with an intensity of $I \ ( \mathbf{m}^{-2} \bullet\mathbf{s}^{-1} )$ is incident on an infinite slab with a thickness of $a$. What is the probability of neutrons eventually diffusing through the slab?

Options:
A. $$
\frac{L D} {2 \sinh ( a / L ) + L \cosh ( a / L )}
$$
B. $$
\frac{L\sinh ( a / L )} {D + 2 \cosh ( a / L )}
$$
C. $$
\frac{2 D} {L \cosh ( a / L )+2 D \sinh ( a / L )}
$$
D. $$
\frac{D - L} {L \cosh ( a / L )- D \sinh ( a / L )}
$$
E. $$
\frac{L} {2 D + \cosh ( a / L ) \sinh ( a / L )}
$$
F. $$
\frac{D \cosh ( a / D )} {L + 2 D \sinh ( a / L )}
$$
G. $$
\frac{2 L} {D \tanh ( a / L ) + L}
$$
H. $$
\frac{D \sinh ( a / L )} {L + 2 D \cosh ( a / L )}
$$
I. $$
\frac{D L} {2 \cosh ( a / L ) + D \sinh ( a / L )}
$$
J. $$
\frac{2 \sinh ( a / D )} {L \cosh ( a / L ) + D}
$$
Answer: C
A spherical bare reactor, in which the fuel "U" (density $1.87 \times 10^{3} \mathrm{~kg/m^{3}}$) is uniformly distributed in graphite, with an atomic number ratio of $N_{\mathrm{c}} / N_{5} = 10^{4}$. The relevant cross-section data are as follows: $\sigma_{n}^{c} = 0.003 \, \mathrm{b}$; $\sigma_{\mathrm{f}}^{5} = 584 \, \mathrm{b}$; $\sigma_{r}^{5} = 105 \, \mathrm{b}$; $\nu = 2.43$, $D = 0.009 \mathrm{~m}$. Using single group theory, estimate what is the critical radius and critical mass of this reactor?

Options:
A. $$
0.520~\mathrm{m},~180~\mathrm{kg}
$$
B. $$
0.480~\mathrm{m},~190~\mathrm{kg}
$$
C. $$
0.530~\mathrm{m},~140~\mathrm{kg}
$$
D. $$
0.450~\mathrm{m},~130~\mathrm{kg}
$$
E. $$
0.514~\mathrm{m},~156~\mathrm{kg}
$$
F. $$
0.620~\mathrm{m},~160~\mathrm{kg}
$$
G. $$
0.570~\mathrm{m},~145~\mathrm{kg}
$$
H. $$
0.600~\mathrm{m},~200~\mathrm{kg}
$$
I. $$
0.400~\mathrm{m},~250~\mathrm{kg}
$$
J. $$
0.700~\mathrm{m},~175~\mathrm{kg}
$$
Answer: E
Consider a spherical fast neutron critical bare reactor composed of pure $^{239} \mathrm{Pu}~ (p=14.4×10^3~ \mathrm{kg/m^3})$. Use the following one-group constants: $\nu=2.19$, $\sigma_{\mathrm{f}}=1.85$ b, $\sigma_{\mathrm{r}}=0.26$ b, $\sigma_{\mathrm{tr}}=6.8$ b. What are its critical radius and critical mass?

Options:
A. $$80.5~\mathrm{kg}$$
B. $$65.4~\mathrm{kg}$$
C. $$71.9~\mathrm{kg}$$
D. $$69.5~\mathrm{kg}$$
E. $$110.2~\mathrm{kg}$$
F. $$84.7~\mathrm{kg}$$
G. $$92.3~\mathrm{kg}$$
H. $$95.0~\mathrm{kg}$$
I. $$77.8~\mathrm{kg}$$
J. $$98.1~\mathrm{kg}$$
Answer: I
When using the method of withdrawing the control rod to push the critical position, if the rod group is raised 12 steps causing the source range count to increase from $n_{1}$ to $n_{2}$ and $n_{2}=1.5 n_{1}$, assuming the differential worth of the control rod is constant, estimate how many more steps are needed to raise the rod group to reach criticality?

Options:
A. $$30$$
B. $$18$$
C. $$36$$
D. $$22$$
E. $$24$$
F. $$32$$
G. $$28$$
H. $$26$$
I. $$20$$
J. $$14$$
Answer: E
Given a cylindrical uranium-water lattice device, $R=0.50 \, \mathrm{m}$, with a water level height of $H=1.0 \, \mathrm{m}$, assume the lattice parameters are: $k_{\infty}=1.19, L^{2}=6.6 \times 10^{-4} \, \mathrm{m}^{2}, \tau=0.50 \times 10^{-2} \, \mathrm{m}^{2}$. Assume a pressurized water reactor uses this uranium-water lattice as the core, with the core dimensions being $R=1.66 \, \mathrm{m}, H=3.5 \, \mathrm{m}$. If the reflector savings are estimated to be $\delta_{\mathbf{r}}=0.07 \, \mathrm{m}, \delta_{\mathrm{H}}=0.1 \, \mathrm{m}$, what is the initial reactivity $\rho_{0}$ of the nuclear reactor?

Options:
A. $$0.1098$$
B. $$0.0952$$
C. $$0.1324$$
D. $$0.1468$$
E. $$0.1457$$
F. $$0.1579$$
G. $$0.1234$$
H. $$0.1783$$
I. $$0.1826$$
J. $$0.1635$$
Answer: D
There is a small nuclear power plant with an electric power output of 150 MW. Suppose the plant's efficiency (the ratio of electric power to thermal power) is 30%. Assuming the fissile nuclide is pure $\mathrm{^{235}U}$ and each fission releases an energy of 200 MeV, how much $235\mathrm{U}$ is consumed by the plant's reactor operating at rated power for 1 hour?

Options:
A. $$
m=0. 0 5 4 0 8 \, \mathrm{k g}
$$
B. $$
m=0. 0 1 6 5 8 \, \mathrm{k g}
$$
C. $$
m=0. 0 3 4 9 8 \, \mathrm{k g}
$$
D. $$
m=0. 0 5 3 6 8 \, \mathrm{k g}
$$
E. $$
m=0. 0 4 1 7 8 \, \mathrm{k g}
$$
F. $$
m=0. 0 4 2 7 8 \, \mathrm{k g}
$$
G. $$
m=0. 0 2 9 3 8 \, \mathrm{k g}
$$
H. $$
m=0. 0 3 5 2 8 \, \mathrm{k g}
$$
I. $$
m=0. 0 1 2 6 8 \, \mathrm{k g}
$$
J. $$
m=0. 0 2 5 6 8 \, \mathrm{k g}
$$
Answer: J
An isotropic point source releases $S$ fast neutrons per second in an infinite moderator, and the thermal neutron flux density $\phi_{2}$ in the two-group theory is given by the following equation __________.

Options:
A. $$
\phi_{2} ( r )=\frac{S \mathrm{L}^{2}} {4 \pi r \tau D_{2} ( L^{2}-1)} ( \mathrm{e}^{r / L}-\mathrm{e}^{-r / \tau} )
$$
B. $$
\phi_{2} ( r )=\frac{S L^{2}} {4 \pi r D_{2} ( L^{2}+1)} ( \mathrm{e}^{-r / \tau}-\mathrm{e}^{-r / L} )
$$
C. $$
\phi_{2} ( r )=\frac{S \mathrm{L}^{2}} {2 \pi r D_{2} ( L^{2}-\tau)} ( \mathrm{e}^{-r / \tau}-\mathrm{e}^{-r / L} )
$$
D. $$
\phi_{2} ( r )=\frac{S \mathrm{L}^{2}} {4 \pi \tau r D_{2} ( L^{2}-\tau)} ( \mathrm{e}^{-r / \sqrt{L}}-\mathrm{e}^{-r / L} )
$$
E. $$
\phi_{2} ( r )=\frac{S \mathrm{L}^{2}} {4 \pi r D_{2} ( L^{2}-\tau)} ( \mathrm{e}^{-r / L}-\mathrm{e}^{-r / \sqrt{\tau}} )
$$
F. $$
\phi_{2} ( r )=\frac{S \tau L^{2}} {4 \pi r D_{2} ( L^{2}-1)} ( \mathrm{e}^{-r / L}-\mathrm{e}^{r / \tau} )
$$
G. $$
\phi_{2} ( r )=\frac{S \mathrm{L}^{2}} {4 \pi r D_{2} ( \tau-L^{2})} ( \mathrm{e}^{r / L}-\mathrm{e}^{-r / \tau} )
$$
H. $$
\phi_{2} ( r )=\frac{S \mathrm{L}^{2}} {4 \pi r \tau D_{2} ( 1-L^{2})} ( \mathrm{e}^{-r / L}+\mathrm{e}^{-r / \tau} )
$$
I. $$
\phi_{2} ( r )=\frac{S \tau^{2}} {4 \pi r D_{2} ( L^{2}-\mathrm{L})} ( \mathrm{e}^{-r / \tau}-\mathrm{e}^{-r / L} )
$$
J. $$
\phi_{2} ( r )=\frac{S \mathrm{L}^{2}} {4 \pi r D_{2} ( \tau-L^{2})} ( \mathrm{e}^{-r / L}-\mathrm{e}^{-r / \tau} )
$$
Answer: E
Air at a pressure of 7.0 MPa and a temperature of 40°C undergoes isentropic expansion to a pressure of 0.1 MPa. Calculate the outlet temperature of the expander and the work done.

Options:
A. $$-180°C,154.6856kJ$$
B. $$-165°C,162.9149kJ$$
C. $$-175°C,160.3420kJ$$
D. $$-168°C,159.1128kJ$$
E. $$-181°C,158.5675kJ$$
F. $$-183°C,161.5043kJ$$
G. $$-190°C,157.2215kJ$$
H. $$-187°C,153.4732kJ$$
I. $$-174°C,156.2990kJ$$
J. $$-178°C,155.7680kJ$$
Answer: E
The cavity length of a certain solid-state laser is 45 cm, with a medium length of 30 cm and a refractive index $\mathbf{n}=1.5$. Given that the total one-way loss rate of this cavity is $0.01 \pi$, determine the mode linewidth of the passive cavity's intrinsic longitudinal modes for this laser is____.

Options:
A. $$
4. 2 M H z
$$
B. $$
8. 3 M H z
$$
C. $$
2. 5 M H z
$$
D. $$
5. 5 M H z
$$
E. $$
7. 4 M H z
$$
F. $$
3. 7 M H z
$$
G. $$
9. 9 M H z
$$
H. $$
1. 8 M H z
$$
I. $$
6. 1 M H z
$$
J. $$
3. 0 M H z
$$
Answer: C
In a ruby $Q$-switched laser, it is possible to excite nearly all of the $\mathrm{Cr}^{+3}$ to the laser upper energy level and produce giant laser pulses. Suppose the ruby rod has a diameter of 1 cm, a length of 7.5 cm, and a $\mathrm{Cr}^{+3}$ concentration of $2 \times 10^{19} \mathrm{cm}^{-3}$. With a pulse width of 10 ns, determine the maximum energy and pulse power of the output laser. Answer is____.

Options:
A. $$
1. 9 \times1 0^{-9} J
$$
$$
0. 2 8 w
$$
B. $$
5. 2 \times1 0^{-9} J
$$
$$
0. 5 5 w
$$
C. $$
2. 8 \times1 0^{-9} J
$$
$$
0. 5 0 w
$$
D. $$
5. 0 \times1 0^{-9} J
$$
$$
0. 1 2 w
$$
E. $$
3. 9 \times1 0^{-9} J
$$
$$
0. 3 0 w
$$
F. $$
3. 1 \times1 0^{-9} J
$$
$$
0. 2 0 w
$$
G. $$
3. 4 \times1 0^{-9} J
$$
$$
0. 3 4 w
$$
H. $$
4. 1 \times1 0^{-9} J
$$
$$
0. 2 3 w
$$
I. $$
2. 5 \times1 0^{-9} J
$$
$$
0. 4 5 w
$$
J. $$
4. 5 \times1 0^{-9} J
$$
$$
0. 4 0 w
$$
Answer: G
The cavity length of the helium-neon laser is 1 m, and the discharge tube diameter is 2 mm. The reflectivities of the two mirrors are 100% and 98%, with a single-pass diffraction loss rate of $8 = 0.04$. Given that $I_c = 0.1 \text{ W/mm}^2$, $\mathbf{G}_{\mathrm{m}} = 3 \times 10^{-4} / \mathbf{d}$, calculate the single-mode output power for $\textcircled{1} \mathbf{v}_{\mathrm{q}} = \mathbf{v}_{0}$ and the single-mode output power for $\textcircled{2} \mathbf{v}_{\mathrm{q}} = \mathbf{v}_{0} + \frac{1}{2} \Delta \mathbf{v}_{\mathrm{D}}$. Answer is____.

Options:
A. $$
2 5. 6 0 m w
$$
$$
7. 7 m w
$$
B. $$
2 6. 0 5 m w
$$
$$
8. 0 m w
$$
C. $$
2 5. 8 5 m w
$$
$$
8. 2 m w
$$
D. $$
2 4. 5 9 m w
$$
$$
7. 9 m w
$$
E. $$
2 6. 4 3 m w
$$
$$
8. 3 m w
$$
F. $$
2 3. 7 1 m w
$$
$$
7. 6 m w
$$
G. $$
2 4. 2 4 m w
$$
$$
7. 2 m w
$$
H. $$
2 4. 9 8 m w
$$
$$
7. 5 m w
$$
I. $$
2 3. 4 7 m w
$$
$$
7. 1 m w
$$
J. $$
2 5. 1 3 m w
$$
$$
7. 8 m w
$$
Answer: J
Diameter of the helium-neon laser discharge tube $\mathbf{d=0.5 \, \text{mm}}$, length $l=10 \, \text{cm}$; the reflectivity of the two mirrors is 100% and 98% respectively, neglecting other losses, with a steady-state power output of $0.5 \, \text{mW}$. Find the number of photons in the cavity. (Assume that there is only one mode $\mathbf{v}_{0}$ in the cavity, and the beam inside is uniform in thickness.)
Answer is___.

Options:
A. $$
6.5 \times 10^{7} units
$$
B. $$
5.3 \times 10^{7} units
$$
C. $$
7.0 \times 10^{7} units
$$
D. $$
6.2 \times 10^{7} units
$$
E. $$
5.0 \times 10^{7} units
$$
F. $$
5.1 \times 10^{7} units
$$
G. $$
4.8 \times 10^{7} units
$$
H. $$
4.5 \times 10^{7} units
$$
I. $$
5.7 \times 10^{7} units
$$
J. $$
3.9 \times 10^{7} units
$$
Answer: B
In a plano-concave cavity, the radius of curvature of the concave mirror is $\mathbf{R}$, and the cavity length $\mathbf{L}=0.2 \mathbf{R}$. Given the wavelength of light, find the waist spot radius of the fundamental mode Gaussian beam excited by this plano-concave cavity is___.

Options:
A. $$
\sqrt{\frac{0. 8 R \lambda} {\pi}}
$$
B. $$
\sqrt{\frac{0. 6 R \lambda} {\pi}}
$$
C. $$
\sqrt{\frac{0. 4 R \lambda} {\pi}}
$$
D. $$
\sqrt{\frac{0. 2 R \lambda} {\pi}}
$$
E. $$
\sqrt{\frac{0. 9 R \lambda} {\pi}}
$$
F. $$
\sqrt{\frac{0. 1 R \lambda} {\pi}}
$$
G. $$
\sqrt{\frac{0. 3 R \lambda} {\pi}}
$$
H. $$
\sqrt{\frac{0. 7 R \lambda} {\pi}}
$$
I. $$
\sqrt{\frac{1. 0 R \lambda} {\pi}}
$$
J. $$
\sqrt{\frac{0. 5 R \lambda} {\pi}}
$$
Answer: C
A double-concave resonant cavity is formed using two concave mirrors, with mirror radii of $\mathbf{R}_{1}=1 \mathbf{m}$ and $\mathbf{R}_{2}=2 \mathbf{m}$, and a cavity length of $\mathbf{L=0.5 \, m}$. How should the waist radius and waist position of a Gaussian beam be chosen to ensure that it becomes a self-reproducing beam within the cavity? (Assume the wavelength of the light is $\lambda=10.6 \, \mu\mathrm{m}$)

Options:
A. $$
1. 26 \ \text{mm}
$$
$$
Left side
27.5 \ \text{cm}
$$
B. $$
1. 28 \ \text{mm}
$$
$$
Right side
37.5 \ \text{cm}
$$
C. $$
1. 22 \ \text{mm}
$$
$$
Center
40.0 \ \text{cm}
$$
D. $$
1. 34 \ \text{mm}
$$
$$
Right side
30.0 \ \text{cm}
$$
E. $$
1. 35 \ \text{mm}
$$
$$
Right side
20.0 \ \text{cm}
$$
F. $$
1. 25 \ \text{mm}
$$
$$
Left side
55.0 \ \text{cm}
$$
G. $$
1. 30 \ \text{mm}
$$
$$
Left side
42.5 \ \text{cm}
$$
H. $$
1. 20 \ \text{mm}
$$
$$
Left side
50.0 \ \text{cm}
$$
I. $$
1. 24 \ \text{mm}
$$
$$
Center
35.0 \ \text{cm}
$$
J. $$
1. 32 \ \text{mm}
$$
$$
Center
25.0 \ \text{cm}
$$
Answer: B
To achieve a coherent length of 1m for a helium-neon laser, what should be its monochromaticity $$\Delta\lambda/\lambda$$?

Options:
A. $$
1. 2 5 6 {\times} 1 0^{-1 0}
$$
B. $$
3. 4 5 6 {\times} 1 0^{-9}
$$
C. $$
9. 0 3 4 {\times} 1 0^{-8}
$$
D. $$
4. 1 5 0 {\times} 1 0^{-9}
$$
E. $$
7. 2 2 3 {\times} 1 0^{-1 1}
$$
F. $$
5. 8 7 7 {\times} 1 0^{-9}
$$
G. $$
6. 3 2 1{\times} 1 0^{-1 2}
$$
H. $$
8. 9 0 1 {\times} 1 0^{-8}
$$
I. $$
2. 6 4 9 {\times} 1 0^{-1 1}
$$
J. $$
6. 3 2 8 {\times} 1 0^{-1 0}
$$
Answer: J
Calculate, under ideal conditions, what is the maximum possible light energy obtainable from a neodymium glass laser with a length of 10 cm, a cross-sectional area of $1 \, \mathrm{cm}^{2}$, and a $\mathrm{Nd}^{3+}$ content of 1% (by weight)? (The density of the neodymium glass is $\rho_{g}=2.6 \, \mathrm{g/cm}^{3}$).
Answer is___.

Options:
A. $$
1 9 0 \mathbf{J}
$$
B. $$
2 3 0 \mathbf{J}
$$
C. $$
2 9 0 \mathbf{J}
$$
D. $$
1 9 8 \mathbf{J}
$$
E. $$
2 2 0 \mathbf{J}
$$
F. $$
2 4 0 \mathbf{J}
$$
G. $$
1 7 5 \mathbf{J}
$$
H. $$
2 1 5 \mathbf{J}
$$
I. $$
1 8 5 \mathbf{J}
$$
J. $$
2 0 4 \mathbf{J}
$$
Answer: J
(Weather Forecast Problem) If the possibility of rain tomorrow is only related to today's weather (whether it rains) and unrelated to the past weather, and let the probability of it raining today and tomorrow be $α$, and the probability of it not raining today but raining tomorrow be $\beta$. Find the probability that it rains today and still rains on the fourth day.

Options:
A. 0.4893
B. 0.4562
C. 0.5174
D. 0.5397
E. 0.5749
F. 0.5883
G. 0.6281
H. 0.4951
I. 0.5120
J. 0.6058
Answer: E
Select a number $X$ randomly from $1, 2, 3, \cdots, n$, and then select another number $Y$ randomly from $1, 2, \cdots, X$. Find $E[Y]$ is ().

Options:
A. $$
\frac{n+6} {4}
$$
B. $$
\frac{n+2} {3}
$$
C. $$
\frac{3n+2} {6}
$$
D. $$
\frac{n+7} {5}
$$
E. $$
\frac{n+5} {3}
$$
F. $$
\frac{4n+1} {8}
$$
G. $$
\frac{n+1} {2}
$$
H. $$
\frac{n+3} {4}
$$
I. $$
\frac{2n+1} {5}
$$
J. $$
\frac{n+4} {3}
$$
Answer: H
Given the velocity distribution and density distribution of a flow field are
$$
u=\frac{x} {r^{3}} \:, \: \: v=\frac{y} {r^{3}} \:, \: \: \: w=\frac{z} {r^{3}}
$$
and
$$\rho=k ( r^{3}-c t ),$$
where $r^{2}=x^{2}+y^{2}+z^{2}$, and $k$ is a non-zero constant.
The local derivative and the substantial derivative of fluid mass in the volume $0 < r \leqslant a$ are ( ) and ( ), respectively.

Options:
A. $$
- 4 k \pi a^{3}
$$
$$
4k \pi a^{3}
$$
B. $$
3 k \pi c t.
$$
$$
6k \pi a^{3}.
$$
C. $$
4 k \pi a^{2}.
$$
$$
8 k \pi a^{3}.
$$
D. $$
- 2 k \pi a^{3}.
$$
$$
8k \pi a^{3}.
$$
E. $$
- 4 k a^{2}.
$$
$$
2k \pi a^{3}.
$$
F. $$
- 4 k \pi a^{3}.
$$
$$
- k \pi a^{3}.
$$
G. $$
4 k a^{3}.
$$
$$
- 4k \pi c t.
$$
H. $$
5 k \pi a^{3}.
$$
$$
3k \pi a^{3}.
$$
I. $$
- 4 \pi a^{2}.
$$
$$
12k \pi a^{3}.
$$
J. $$
- 3 k \pi a^{3}.
$$
$$
6 k \pi a^{3}.
$$
Answer: A
Consider the plane steady flow of an ideal incompressible homogeneous fluid, and let $\psi=a x^{2} y+x^{2}+y^{2}+y$ be the stream function in a certain gravitational field. If the fluid density is $\rho$, the pressure difference of the fluid between points $A ( 1, 2 )$ and $B ( 3, 4 )$ is ( ) .

Options:
A. $$
-44\rho
$$
B. $$
-40\rho
$$
C. $$
-36\rho
$$
D. $$
-42\rho
$$
E. $$
-50\rho
$$
F. $$
-48\rho
$$
G. $$
-46\rho
$$
H. $$
-52\rho
$$
I. $$
+44\rho
$$
J. $$
-38\rho
$$
Answer: A
A cylindrical container with an open top has a height of 0.6m and a diameter of 0.45m. Initially filled with water before rotating, it is now spinning about its vertical central axis at a constant angular velocity $\omega$. The angular velocity when the center of the water surface just touches the bottom is ( ) .

Options:
A. $$
1 6. 5 4 \mathrm{r a d / s ;}
$$
B. $$
1 0. 9 4 \mathrm{r a d / s ;}
$$
C. $$
2 5. 0 4 \mathrm{r a d / s ;}
$$
D. $$
1 5. 2 4 \mathrm{r a d / s ;}
$$
E. $$
1 9. 8 4 \mathrm{r a d / s ;}
$$
F. $$
1 2. 3 4 \mathrm{r a d / s ;}
$$
G. $$
1 8. 7 4 \mathrm{r a d / s ;}
$$
H. $$
1 3. 7 4 \mathrm{r a d / s ;}
$$
I. $$
2 1. 2 4 \mathrm{r a d / s ;}
$$
J. $$
2 3. 6 4 \mathrm{r a d / s ;}
$$
Answer: D
A compressible fluid flows through a circular tube of uniform diameter, with an axial velocity distribution given as:
$$
u = \frac{u_{1} + u_{2}}{2} + \frac{u_{2} - u_{1}}{2} \tanh x,
$$
where $u_{1}$ and $u_{2}$ are the velocities as $x$ approaches negative infinity and positive infinity, respectively. Assume that at any spatial point, the density does not change over time, and the density at $x$ approaching infinity is $\rho = \rho_1$. Give the distribution equation for the density along the pipeline (cross-sectional average density).

Options:
A. $$
\rho_{1} u_{2} / \Bigl( \frac{u_{1}-u_{2}} {2}+\frac{u_{2}+u_{1}} {2} \operatorname{t a n h} x \Bigr).
$$
B. $$
\rho_{2} u_{2} / \Bigl( \frac{u_{1}+u_{1}} {2}+\frac{u_{2}-u_{2}} {2} \operatorname{t a n h} x \Bigr).
$$
C. $$
\rho_{1} + u_{1} / \Bigl( \frac{u_{2}-u_{1}} {2}+\frac{u_{1}+u_{2}} {2} \operatorname{t a n h} x \Bigr).
$$
D. $$
\rho = \rho_{1} u_{1} / \Bigl( \frac{u_{1}+u_{2}} {2}+\frac{u_{2}-u_{1}} {2} \operatorname{t a n h} x \Bigr).
$$
E. $$
\rho_{2} u_{2} / \Bigl( \frac{u_{1}-u_{1}} {2}+\frac{u_{2}+u_{2}} {2} \operatorname{t a n h} x \Bigr).
$$
F. $$
\rho_{2} u_{2} / \Bigl( \frac{u_{2}+u_{1}} {2}+\frac{u_{1}-u_{2}} {2} \operatorname{t a n h} x \Bigr).
$$
G. $$
\rho_{1} u_{1} / \Bigl( \frac{u_{2}-u_{2}} {2}+\frac{u_{1}+u_{1}} {2} \operatorname{t a n h} x \Bigr).
$$
H. $$
\rho_{2} + u_{2} / \Bigl( \frac{u_{1}+u_{2}} {2}+\frac{u_{2}-u_{1}} {2} \operatorname{t a n h} x \Bigr).
$$
I. $$
\rho_{1} u_{1} / \Bigl( \frac{u_{2}+u_{2}} {2}+\frac{u_{1}-u_{1}} {2} \operatorname{t a n h} x \Bigr).
$$
J. $$
\rho_{2} u_{1} / \Bigl( \frac{u_{2}+u_{1}} {2}+\frac{u_{1}-u_{2}} {2} \operatorname{t a n h} x \Bigr).
$$
Answer: D
A spherical droplet with a viscosity coefficient of $\mu$ is descending at a constant speed due to gravity in a stationary fluid with a viscosity coefficient of $\mu_{0}$. Given that the radius of the droplet is $a$, and the densities of the droplet and the fluid are $\rho$ and $\rho_{0}$ respectively, determine the resistance force experienced by the droplet.

Options:
A. $$
\frac{4} {3} \pi\left( \rho-\rho_{0} \right) g a^{3}
$$
B. $$
2 \pi \left( \rho-\rho_{0} \right) \mu g a^{3} $$
C. $$
6 \pi \mu a^{2} \left( \rho-\rho_{0} \right) g $$
D. $$
\frac{2}{3} \pi \mu \rho g a^{3} $$
E. $$
\frac{4}{3} \pi \rho_{0} g a^{3} $$
F. $$
4 \pi \mu_{0} \left( \rho_{0} - \rho \right) g a^{2} $$
G. $$
\frac{5}{3} \pi a^{3} \left( \rho + \rho_{0} \right) g $$
H. $$
\frac{3}{4} \pi \left( \rho_{0} + \rho \right) g a^{3} $$
I. $$
5 \pi \mu_{0} g a \left( \rho - \rho_{0} \right) $$
J. $$
3 \pi \left( \rho_{0} - \rho \right) g a^{2} $$
Answer: A
Outside a stationary cylinder with a radius of $a$, there is a stationary point vortex with strength $\varGamma$. Let the distance from the point vortex to the center of the cylinder be $b$. Give the resultant force exerted by the fluid on the unit length of the cylinder.
( Assume the fluid outside the cylinder is ideal, incompressible, and homogeneous. )

Options:
A. $$
\frac{\rho\Gamma^{2} b^{2}} {2 \pi a \left( a^{2}-b^{2} \right)}
$$
B. $$
\frac{\rho\Gamma^{2} b^{2}} {2 \pi b \left( b^{2}-a^{2} \right)}
$$
C. $$
\frac{\rho\Gamma a^{2}} {2 \pi b \left( b^{2}-a^{2} \right)}
$$
D. $$
\frac{\rho\Gamma^{2} a^{3}} {2 \pi b \left( b^{2}-a^{3} \right)}
$$
E. $$
\frac{\rho\Gamma^{2} b^{2}} {2 \pi a \left( b^{2}-a^{2} \right)}
$$
F. $$
\frac{\rho\Gamma^{2} a^{2}} {2 \pi b \left( a^{2}+b^{2} \right)}
$$
G. $$
\frac{\rho a^{2} \Gamma^{2}} {2 \pi b \left( a^{2}-b^{2} \right)}
$$
H. $$
\frac{\rho\Gamma^{2} a^{2}} {2 \pi a \left( b^{2}-a^{2} \right)}
$$
I. $$
\frac{\rho\Gamma^{2} a^{2}} {2 \pi b \left( b^{2}-a^{2} \right)}
$$
J. $$
\frac{\rho\Gamma^{2} b^{2}} {2 \pi b \left( a^{2}+b^{2} \right)}
$$
Answer: I
What is the order of flexibility for PS, PP, and PE?

Options:
A. $$
\mathrm{P E} = \mathrm{P S} < \mathrm{P P}
$$
B. $$
\mathrm{P P} = \mathrm{P E} < \mathrm{P S}
$$
C. $$
\mathrm{P S} < \mathrm{P P} < \mathrm{P E}
$$
D. $$
\mathrm{P E} < \mathrm{P S} < \mathrm{P P}
$$
E. $$
\mathrm{P P} < \mathrm{P S} < \mathrm{P E}
$$
F. $$
\mathrm{P S} = \mathrm{P P} < \mathrm{P E}
$$
G. $$
\mathrm{P S} < \mathrm{P E} = \mathrm{P P}
$$
H. $$
\mathrm{P P} < \mathrm{P E} < \mathrm{P S}
$$
I. $$
\mathrm{P S} < \mathrm{P E} < \mathrm{P P}
$$
J. $$
\mathrm{P E} < \mathrm{P P} < \mathrm{P S}
$$
Answer: C
Given that polypropylene containing a nucleating agent forms spherulites during isothermal crystallization, the Avrami index $n$ is ().

Options:
A. 4
B. 5
C. 2
D. 7
E. 3
F. 8
G. 9
H. 1
I. 10
J. 6
Answer: E
Given that the unit cell parameters for polymethyl methacrylate are $a \times b \times c = 2.108 \times 1.217 \times 1.055 \,\, \mathrm{nm}, \, \alpha = \beta = \gamma = 90°$, and the measured density is $\rho = 1.23 \,\, \mathrm{g/cm}^{3}$, with $M_{0} = 100.1$, try to determine the number of repeating structural units in each unit cell is ().

Options:
A. 25
B. 45
C. 20
D. 10
E. 55
F. 50
G. 35
H. 30
I. 40
J. 15
Answer: C
The experimentally measured flow activation energies of natural rubber with different relative molecular masses are 25.08 kJ/mol, 40.13 kJ/mol, 53.50 kJ/mol, and 53.90 kJ/mol (repeating unit), respectively, while the heat of evaporation of the monomer isoprene is 25.08 kJ/mol. It is known that the relationship between the flow activation energy $( \Delta E_{\eta} )$ of isoprene and the heat of evaporation $( \Delta H_{V} )$ is given by
$$
\Delta E_{\eta}=\frac{1}{4} \Delta H_{V}
$$
If the flow activation energy of natural rubber is measured to be 54.30 kJ/mol, what is the approximate relative molecular mass of the macromolecular chain segment of the natural rubber?

Options:
A. 720
B. 465
C. 590
D. 580
E. 525
F. 603
G. 650
H. 550
I. 712
J. 480
Answer: F
Three polymers with different relative molecular masses, Sample 1, Sample 2, and Sample 3, have relative molecular masses of $M_{1}, M_{2},$ and $M_{3}$ respectively, where $M_{1} > M_{2} > M_{3}$. The concentration order of their critical mixing point $\varPhi_{2 \mathrm{c}}$ is ().
(a) Sample 1 (b) Sample 2 (c) Sample 3

Options:
A. $$
( a ) > ( c ) > ( b )
$$
B. $$
( c ) > ( b ) > ( a )
$$
C. $$
( b ) > ( c ) > ( a )
$$
D. $$
( c ) > ( a ) > ( b )
$$
E. $$
( a ) > ( b ) > ( c )
$$
F. $$
( b ) > ( a ) > ( c )
$$
Answer: B
A crosslinked rubber, with a relative molecular mass of 500,000 before crosslinking, has $M_{\mathrm{c}}$ of 10,000 after crosslinking. At $25^{\circ} \mathrm{C}$, its density is measured to be $1 \mathrm{g} \cdot \mathrm{cm}^{-3}$. Calculate the Young's modulus of this crosslinked rubber when $\lambda$ is 2?

Options:
A. $$ 4. 0 0 0 \times 1 0^{5} \mathrm{~N / m^{2} ~} $$
B. $$ 3. 7 5 0 \times 1 0^{5} \mathrm{~N / m^{2} ~} $$
C. $$ 4. 1 5 0 \times 1 0^{5} \mathrm{~N / m^{2} ~} $$
D. $$ 2. 3 5 0 \times 1 0^{5} \mathrm{~N / m^{2} ~} $$
E. $$
2. 9 7 5 \times1 0^{5} \mathrm{~ N / m^{2} ~}
$$
F. $$ 5. 4 9 0 \times 1 0^{5} \mathrm{~N / m^{2} ~} $$
G. $$ 2. 8 9 0 \times 1 0^{5} \mathrm{~N / m^{2} ~} $$
H. $$ 1. 2 5 0 \times 1 0^{5} \mathrm{~N / m^{2} ~} $$
I. $$ 1. 8 0 0 \times 1 0^{5} \mathrm{~N / m^{2} ~} $$
J. $$ 3. 4 0 0 \times 1 0^{5} \mathrm{~N / m^{2} ~} $$
Answer: E
When zinc powder is co-boiled with polyvinyl chloride in dioxane, infrared spectroscopy indicates that the product contains cyclopropane structures but no double bonds. Therefore, the bond sequence of the structural unit of polyvinyl chloride before the reaction is ( ).

Options:
A. Atactic configuration
B. Syndiotactic linkage
C. Branched polymer structure
D. Head-to-head coupling
E. Isotactic arrangement
F. Cross-linked network
G. Random copolymer pattern
H. Tail-to-head coupling
I. Alternating copolymer sequence
J. Head-to-tail coupling
Answer: J
Assuming the stress relaxation behavior of a certain polymer follows the Maxwell model (series model), where the modulus of the spring is $10^0 \, \mathrm{Pa}$ and the viscosity of the dashpot is $10^{10} \, \mathrm{Pa} \cdot \mathrm{s}$, if a certain stress is applied at time $t=0$, causing an instantaneous strain of $1\%$, and the constant strain of $1\%$ is maintained, calculate the stress at $t=50 \, \mathrm{s}$ is ().

Options:
A. $$1.2\times10^6\text{ Pa}$$
B. $$3.9\times10^9\text{ Pa}$$
C. $$7.3\times10^8\text{ Pa}$$
D. $$6.1\times10^7\text{ Pa}$$
E. $$4.4\times10^7\text{ Pa}$$
F. $$8.2\times10^3\text{ Pa}$$
G. $$5.5\times10^7\text{ Pa}$$
H. $$9.8\times10^5\text{ Pa}$$
I. $$2.7\times10^6\text{ Pa}$$
J. $$1.5\times10^9\text{ Pa}$$
Answer: D
Below the glass transition temperature, the free volume of the polymer decreases as the temperature drops ().

Options:
A. Reduce elasticity
B. Enhance conduction
C. Trigger cross-linking
D. Increase significantly
E. Support chain mobility
F. Widen glassy state
G. Facilitate expansion
H. Enable plasticity
I. Encourage crystallization
J. Remain unchanged
Answer: J
The modulus of cross-linked rubber decreases as the temperature increases.

Options:
A. Contract
B. Condense
C. Compress
D. Rise
E. Shrink
F. Amplify
G. Solidify
H. Freeze
I. Harden
J. Thicken
Answer: D
Voigt model (parallel) can be used to describe ().

Options:
A. The Solubility Equilibrium of Salt Solutions
B. The Healing Process in Metallic Alloys
C. The Thermal Expansion of Pure Metals
D. The Stress-Strain Curve of Soft Tissues
E. The Diffusion Rate in Gaseous Mixtures
F. The Magnetic Permeability of Ferrous Materials
G. The Oscillation Frequency of Quartz Crystals
H. The Electrical Conductivity of Insulators
I. The Evaporation Rate of Volatile Liquids
J. The Creep Process of Cross-linked Polymers
Answer: J
In the silver pattern, the orientation of the molecular chain should be () with the external force .

Options:
A. Variable
B. Erratic
C. Parallel
D. Chaotic
E. Disjointed
F. Consistent
G. Reverse
H. Transverse
I. Perpendicular
J. Random
Answer: F
Rubber will () during the process of elongation.

Options:
A. Endothermic
B. Equilibrium
C. Excrete
D. Electronegative
E. Electrify
F. Elastic
G. Enzyme
H. Erosion
I. Exothermic
J. Evaporate
Answer: I
Given that at 18°C, the equivalent conductance of a 1.0×10⁻⁴ eq/dm³ NaI solution is $127 \mathrm{~ S cm^{2} / eq}$, and $\lambda_{0} \left( \mathrm{~ Na^{+} ~} \right)=50$ . $1 \mathrm{~ S cm^{2} / eq}$, $\lambda_{0} \left( \mathrm{Cl}^{-} \right)=76.3 \mathrm{~ S cm^{2} / eq}$. The transport number of the $\mathrm{I}^{-}$ ion in this solution is().

Options:
A. $$
= 0. 5 7 2
$$
B. $$
= 0. 6 2 9
$$
C. $$
= 0. 6 1 4
$$
D. $$
= 0. 7 0 2
$$
E. $$
= 0. 5 5 0
$$
F. $$
= 0. 6 3 5
$$
G. $$
= 0. 4 8 9
$$
H. $$
= 0. 5 9 8
$$
I. $$
= 0. 5 8 3
$$
J. $$
= 0. 6 0 6
$$
Answer: J
After subtracting the conductivity of water, the conductivity of a saturated Cu$(OH)_{\mathrm{2}}$ solution at 18°C is $1.19 \times 10^{-5} \mathrm{S/cm}$. Use this value to calculate the solubility product $K_{\mathrm{S}}$ of Cu$(OH)_{\mathrm{2}}$ in water at this temperature. It is known that the molar conductivity of Cu$(OH)_{\mathrm{2}}$ is 87.3 Scm$^{2}$/mol is().

Options:
A. $$
= 6. 5 1 0 \times1 0^{-8} \ ( \mathrm{m o l} / \mathrm{d m}^{3} )^{3}
$$
B. $$
= 5. 2 3 4 \times1 0^{-1 2} \ ( \mathrm{m o l} / \mathrm{d m}^{3} )^{3}
$$
C. $$
= 8. 1 1 9 \times1 0^{-1 0} \ ( \mathrm{m o l} / \mathrm{d m}^{3} )^{3}
$$
D. $$
= 1. 0 0 6 \times1 0^{-1 1} \ ( \mathrm{m o l} / \mathrm{d m}^{3} )^{3}
$$
E. $$
= 7. 0 0 5 \times1 0^{-1 0} \ ( \mathrm{m o l} / \mathrm{d m}^{3} )^{3}
$$
F. $$
= 9. 4 8 7 \times1 0^{-1 1} \ ( \mathrm{m o l} / \mathrm{d m}^{3} )^{3}
$$
G. $$
= 4. 9 9 6 \times1 0^{-9} \ ( \mathrm{m o l} / \mathrm{d m}^{3} )^{3}
$$
H. $$
= 3. 5 9 8 \times1 0^{-8} \ ( \mathrm{m o l} / \mathrm{d m}^{3} )^{3}
$$
I. $$
= 2. 0 1 2 \times1 0^{-9} \ ( \mathrm{m o l} / \mathrm{d m}^{3} )^{3}
$$
J. $$
= 2. 7 3 2 \times1 0^{-1 0} \ ( \mathrm{m o l} / \mathrm{d m}^{3} )^{3}
$$
Answer: D
Battery $\mathrm{Zn} \, | \, \mathrm{ZnSO}_{4} \, ( \, a_{1}=1 \, ) \, |$ Cu$SO_{4}$ $( a_{2}=1 ) \mid\mathrm{Cu}$ has electromotive forces of 1.101 $\mathbf{V}$ and 1.103 $\mathbf{V}$ at 20°C and 25°C, respectively. The $\mathbf{Q}_{p}$, ∆H, and equilibrium constant $K$ for this galvanic cell at 20°C is().

Options:
A. $$
Q p=\Delta H=-1 8 1. 2 k J / m o l;K=1 1. 2 \times1 0^{3 3}
$$
B. $$
Q p=\Delta H=-1 3 9. 7 k J / m o l;K=2. 1 7 \times1 0^{3 4}
$$
C. $$
Q p=\Delta H=-1 3 0. 5 k J / m o l;K=9. 5 2 \times1 0^{3 6}
$$
D. $$
Q p=\Delta H=-1 9 5. 3 k J / m o l;K=4. 2 9 \times1 0^{3 4}
$$
E. $$
Q p=\Delta H=-2 0 4. 7 k J / m o l;K=8. 3 8 \times1 0^{3 8}
$$
F. $$
Q p=\Delta H=-1 8 9. 8 k J / m o l;K=7. 9 5 \times1 0^{3 7}
$$
G. $$
Q p=\Delta H=-1 9 9. 5 k J / m o l;K=9. 0 8 \times1 0^{3 1}
$$
H. $$
Q p=\Delta H=-1 4 8. 4 k J / m o l;K=3. 5 6 \times1 0^{3 9}
$$
I. $$
Q p=\Delta H=-1 5 2. 6 k J / m o l;K=6. 0 1 \times1 0^{3 5}
$$
J. $$
Q p=\Delta H=-1 6 8. 9 k J / m o l;K=5. 7 4 \times1 0^{3 2}
$$
Answer: F
An electron beam with a kinetic energy of 1 keV passes through a polycrystalline metal foil to produce diffraction. This metal has a cubic crystal structure with an atomic spacing of 1 Å. What is the wavelength of the electron ?

Options:
A. 0. 4 0 ($^ {}\AA$)
B. 0. 8 7 ($^ {}\AA$)
C. 0. 2 9 ($^ {}\AA$)
D. 0. 3 5 ($^ {}\AA$)
E. 0. 4 8 ($^ {}\AA$)
F. 0. 3 9 ($^ {}\AA$)
G. 0. 7 3 ($^ {}\AA$)
H. 0. 6 1 ($^ {}\AA$)
I. 0. 5 0 ($^ {}\AA$)
J. 0. 9 2 ($^ {}\AA$)
Answer: F
Copper is a monovalent metal with a density of $8000 \mathbf{kg}/\mathbf{m}^3$ and an atomic mass of 64. What is the Fermi energy of electrons at absolute zero in temperature ?

Options:
A. $$
8. 2 {\mathrm{e V}}
$$
B. $$
6. 2 {\mathrm{e V}}
$$
C. $$
5. 9 {\mathrm{e V}}
$$
D. $$
4. 8 {\mathrm{e V}}
$$
E. $$
7. 3 {\mathrm{e V}}
$$
F. $$
8. 0 {\mathrm{e V}}
$$
G. $$
9. 1 {\mathrm{e V}}
$$
H. $$
7. 0 {\mathrm{e V}}
$$
I. $$
6. 5 {\mathrm{e V}}
$$
J. $$
5. 5 {\mathrm{e V}}
$$
Answer: I
The longitudinal effective mass of electrons in semiconductor silicon is $m_{l} = 0.98 m_{0}$, and the transverse effective mass is $m_{t} = 0.19 m_{0}$ ($m_{0}$ is the rest mass of an electron). Given that the electron mobility in silicon is 0.1 m²/V·s, calculate the average free time and the drift distance of silicon electrons as () when an external electric field strength of $10^4$ V/m is applied.

Options:
A. $$
1.48 \times10^{-13} ( \mathrm{s} )
$$
$$
1. 4 8 ^ {}\AA
$$
B. $$
1 . 2 \times1 0^{3} ( \mathrm{m / s} )
$$
$$
1. 2 9 ^ {}\AA
$$
C. $$
2 . 5 \times1 0^{3} ( \mathrm{m / s} )
$$
$$
1. 7 3 ^ {}\AA
$$
D. $$
3 \times1 0^{3} ( \mathrm{m / s} )
$$
$$
1. 3 5 ^ {}\AA
$$
E. $$
1 \times1 0^{4} ( \mathrm{m / s} )
$$
$$
2. 1 0 ^ {}\AA
$$
F. $$
4 \times1 0^{3} ( \mathrm{m / s} )
$$
$$
2. 0 4 ^ {}\AA
$$
G. $$
2 \times1 0^{3} ( \mathrm{m / s} )
$$
$$
2. 5 0 ^ {}\AA
$$
H. $$
0 . 7 5 \times1 0^{3} ( \mathrm{m / s} )
$$
$$
1. 5 5 ^ {}\AA
$$
I. $$
0 . 8 5 \times1 0^{3} ( \mathrm{m / s} )
$$
$$
1. 6 2 ^ {}\AA
$$
J. $$
9 \times1 0^{2} ( \mathrm{m / s} )
$$
$$
1. 8 0 ^ {}\AA
$$
Answer: A
Assume an alkali metal halide, $\varepsilon(0) = 5.9, \varepsilon(\infty) = 2.25$, with a reflectivity $R = 0$ at $\lambda_{0} = 30.6 \mu\mathrm{m}$, and $\varepsilon(\omega)$ is a real number. What is the value of $\omega_{\mathrm{L}}$ ?
( Here $\omega_{\mathrm{L}}$ is the frequency of the long optical longitudinal phonon.)

Options:
A. $$
6. 1 4 \times1 0^{1 3} \mathrm{s}^{-1}
$$
B. $$
6. 3 0 \times1 0^{1 3} \mathrm{s}^{-1}
$$
C. $$
5. 9 5 \times1 0^{1 3} \mathrm{s}^{-1}
$$
D. $$
4. 8 7 \times1 0^{1 3} \mathrm{s}^{-1}
$$
E. $$
5. 7 7 \times1 0^{1 3} \mathrm{s}^{-1}
$$
F. $$
4. 5 6 \times1 0^{1 3} \mathrm{s}^{-1}
$$
G. $$
4. 9 2 \times1 0^{1 3} \mathrm{s}^{-1}
$$
H. $$
5. 0 3 \times1 0^{1 3} \mathrm{s}^{-1}
$$
I. $$
5. 2 0 \times1 0^{1 3} \mathrm{s}^{-1}
$$
J. $$
5. 1 8 \times1 0^{1 3} \mathrm{s}^{-1}
$$
Answer: H
Let the function $f$, with period $2\pi$, be the periodic extension of the function $e^{\alpha x}$ defined on $[0, 2\pi)$, where $\alpha$ is any given non-zero real number. What is the trigonometric Fourier series of $f$?

Options:
A. $$
\frac{e^{3 \pi\alpha}+1} {e^{\pi\alpha}-1}
$$
B. $$
\frac{e^{3 \pi\alpha}-1} {e^{\alpha}+1}
$$
C. $$
\frac{e^{2 \alpha \pi}+1} {2}
$$
D. $$
\frac{e^{2 \pi\alpha}+1} {e^{2 \pi\alpha}-1}
$$
E. $$
\frac{1+e^{2 \pi\alpha}} {1-e^{2 \pi\alpha}}
$$
F. $$
\frac{e^{4 \pi\alpha}-1} {e^{\alpha}+1}
$$
G. $$
\frac{e^{2 \pi\alpha}-1} {e^{2 \pi\alpha}+1}
$$
H. $$
\frac{e^{2 \pi\alpha}+2} {e^{2 \pi\alpha}-2}
$$
I. $$
\frac{e^{\alpha}+e^{-\alpha}} {2}
$$
J. $$
\frac{e^{\pi\alpha}+e^{-\pi\alpha}} {1}
$$
Answer: D
Assuming that the Sculptor group of galaxies occupies a spherical volume of space, what is the difference in magnitude between two identical objects located at the very front and back of the group ?

Options:
A. $$
0. 6 3 5
$$
B. $$
0. 7 2 8
$$
C. $$
0. 9 4 6
$$
D. $$
0. 9 1 0
$$
E. $$
0. 5 9 4
$$
F. $$
0. 8 7 2
$$
G. $$
0. 6 8 9
$$
H. $$
0. 7 6 3
$$
I. $$
0. 7 5 5
$$
J. $$
0. 8 2 5
$$
Answer: I
The radio galaxy Centaurus A has a redshift of $z=0. 0 0 1 5 7$ . The monochromatic flux of Cen A is $F_{v}=9 1 2$ Jy at a frequency of 1400 MHz. Using $\alpha=0. 6$ for its spectral index, estimate what is the radio luminosity of Cen A ?

Options:
A. $$
8 \times1 0^{3 2} \mathrm{~ W}
$$
0.67
B. $$
3 \times1 0^{3 5} \mathrm{~ W}
$$
0.72
C. $$
4 \times1 0^{3 3} \mathrm{~ W}
$$
0.68
D. $$
9 \times1 0^{3 3} \mathrm{~ W}
$$
0.74
E. $$
6 \times1 0^{3 5} \mathrm{~ W}
$$
0.73
F. $$
2 \times1 0^{3 4} \mathrm{~ W}
$$
0.71
G. $$
5 \times1 0^{3 4} \mathrm{~ W}
$$
0.75
H. $$
1 \times1 0^{3 3} \mathrm{~ W}
$$
0.69
I. $$
7 \times1 0^{3 4} \mathrm{~ W}
$$
0.76
J. $$
1 \times1 0^{3 6} \mathrm{~ W}
$$
0.78
Answer: F