MikaStars39/nano-eval huggingface dataset:
When comparing the energy released per nucleon in D-T fusion and uranium fission, the former is approximately is___.

Options:
A. $$
7 times
$$
B. $$
5 times
$$
C. $$
6 times
$$
D. $$
3 times
$$
E. $$
10 times
$$
F. $$
4 times
$$
G. $$
1.5 times
$$
H. $$
9 times
$$
I. $$
2 times
$$
J. $$
8 times
$$
Answer: F
The HCl molecule has a near-infrared spectral band, with the wavenumbers of several adjacent lines given as $\tilde{\nu}_{1} = 2925.78 \, \text{cm}^{-1}$, $\tilde{\nu}_{2} = 2906.25 \, \text{cm}^{-1}$, $\tilde{\nu}_{3} = 2865.09 \, \text{cm}^{-1}$, $\tilde{\nu}_{4} = 2843.56 \, \text{cm}^{-1}$, and $\tilde{\nu}_{5} = 2821.49 \, \text{cm}^{-1}$. The atomic masses of H and Cl are 1.008 and 35 respectively. Given $\boldsymbol{h} = 6.58 \times 10^{-22} \, \text{MeV} \cdot \text{s}$ and $\mathrm{u} = 1.66 \times 10^{-27} \, \text{kg}$, what are the baseline wavenumber $\tilde{\nu}_{0}$ of this spectral band, the moment of inertia of this molecule, and the distance between the two nuclei?

Options:
A. $$2901.23cm^{-1},~2.79\times10^{-47}\mathrm{m^2\cdot kg},~1.30\times10^{-10}\mathrm{m}
$$
B. $$2900.00cm^{-1},~3.00\times10^{-47}\mathrm{m^2\cdot kg},~1.35\times10^{-10}\mathrm{m}
$$
C. $$2870.56cm^{-1},~3.10\times10^{-47}\mathrm{m^2\cdot kg},~1.36\times10^{-10}\mathrm{m}
$$
D. $$2860.45cm^{-1},~2.95\times10^{-47}\mathrm{m^2\cdot kg},~1.31\times10^{-10}\mathrm{m}
$$
E. $$2885.67cm^{-1},~2.87\times10^{-47}\mathrm{m^2\cdot kg},~1.29\times10^{-10}\mathrm{m}
$$
F. $$2885.00cm^{-1},~3.05\times10^{-47}\mathrm{m^2\cdot kg},~1.34\times10^{-10}\mathrm{m}
$$
G. $$2890.67cm^{-1},~2.82\times10^{-47}\mathrm{m^2\cdot kg},~1.32\times10^{-10}\mathrm{m}
$$
H. $$2898.42cm^{-1},~2.75\times10^{-47}\mathrm{m^2\cdot kg},~1.37\times10^{-10}\mathrm{m}
$$
I. $$2867.89cm^{-1},~2.77\times10^{-47}\mathrm{m^2\cdot kg},~1.38\times10^{-10}\mathrm{m}
$$
J. $$2875.12cm^{-1},~2.80\times10^{-47}\mathrm{m^2\cdot kg},~1.33\times10^{-10}\mathrm{m}
$$
Answer: E
When a spin-1/2 ion transitions from paramagnetic to ferromagnetic, the relationship between molar heat capacity and temperature is as follows: when the temperature $T_{0} / 2 \! < \! T \! < \! T_{0}$, $c \!=\! c_{\operatorname* {m a x}} ( 2 T / T_{0} \!-\! 1 )$; otherwise, $c = 0$. Attempt to express $c_{\operatorname* {m a x}}$ using fundamental constants. This is a highly simplified theory. What is the $c_{\operatorname* {m a x}}$ ?

Options:
A. $$
{\frac{R \mathrm{l n} 2} {3-\mathrm{l n} 2}}
$$
B. $$
{\frac{R \mathrm{l n} 5} {2-\mathrm{l n} 2}}
$$
C. $$
{\frac{R \mathrm{l n} 1} {1-\mathrm{l n} 3}}
$$
D. $$
{\frac{1 R \mathrm{l n} 2} {2-\mathrm{l n} 2}}
$$
E. $$
{\frac{2 R \mathrm{l n} 2} {1+\mathrm{l n} 2}}
$$
F. $$
{\frac{3 R \mathrm{l n} 2} {1-\mathrm{l n} 1}}
$$
G. $$
{\frac{R \mathrm{l n} 4} {2-\mathrm{l n} 3}}
$$
H. $$
{\frac{R \mathrm{l n} 2} {1-\mathrm{l n} 2}}
$$
I. $$
{\frac{R \mathrm{l n} 3} {1-\mathrm{l n} 4}}
$$
J. $$
{\frac{2 R \mathrm{l n} 2} {1-\mathrm{l n} 3}}
$$
Answer: H
Consider a diatomic molecule gas composed of two different atoms. The gas is dilute, and the moment of inertia for molecular rotation about an axis through the center of mass and perpendicular to the line joining the two atoms is $I$. Evaluate the contribution of this rotation to the molar entropy in the following two limiting cases:
(1) $k T \gg \hbar^{2} / I$;
(2) $k T \ll \hbar^{2} / I$ ( the lowest-order non-zero contributions ).

Options:
A. $$
k N \Big( 1+\operatorname{l n} {\frac{2 I k T} {3 \hbar^{2}}} \Big)
$$
$$
\approx{\frac{6 N \hbar^{2}} {I T}} E
$$
B. $$
k N \Big( 1+\operatorname{l n} {\frac{4 I k T} {\hbar^{2}}} \Big)
$$
$$
\approx{\frac{2 N \hbar^{2}} {I T}} C
$$
C. $$
k N \Big( 1+\operatorname{l n} {\frac{7 I k T} {\hbar^{2}}} \Big)
$$
$$
\approx{\frac{9 N \hbar^{2}} {I T}} H
$$
D. $$
k N \Big( 1+\operatorname{l n} {\frac{8 I k T} {\hbar^{2}}} \Big)
$$
$$
\approx{\frac{10 N \hbar^{2}} {I T}} I
$$
E. $$
k N \Big( 1+\operatorname{l n} {\frac{9 I k T} {3 \hbar^{2}}} \Big)
$$
$$
\approx{\frac{11 N \hbar^{2}} {I T}} J
$$
F. $$
k N \Big( 1+\operatorname{l n} {\frac{6 I k T} {3 \hbar^{2}}} \Big)
$$
$$
\approx{\frac{8 N \hbar^{2}} {I T}} G
$$
G. $$
k N \Big( 1+\operatorname{l n} {\frac{2 I k T} {\hbar^{2}}} \Big)
$$
$$
\approx{\frac{3 N \hbar^{2}} {I T}} A
$$
H. $$
k N \Big( 1+\operatorname{l n} {\frac{5 I k T} {\hbar^{2}}} \Big)
$$
$$
\approx{\frac{7 N \hbar^{2}} {I T}} F
$$
I. $$
k N \Big( 1+\operatorname{l n} {\frac{I k T} {2 \hbar^{2}}} \Big)
$$
$$
\approx{\frac{4 N \hbar^{2}} {I T}} B
$$
J. $$
k N \Big( 1+\operatorname{l n} {\frac{3 I k T} {2 \hbar^{2}}} \Big)
$$
$$
\approx{\frac{5 N \hbar^{2}} {I T}} D
$$
Answer: G
A system consists of $N$ nearly independent particles each with mass $m$, reaching thermal equilibrium at high temperatures ( obtained using classical statistics ). The particles vibrate one-dimensionally around their equilibrium positions. Determine the heat capacity of the system for the following cases:
(1) The restoring force is proportional to the displacement $x$;
(2) The restoring force is proportional to the cube of the displacement $x$. (The result can be obtained without explicitly calculating the integrals.)

Options:
A. $$
2 N k
$$
$$
\frac{1} {3} N k.
$$
B. $$
5 N k
$$
$$
\frac{3} {2} N k.
$$
C. $$
N k
$$
$$
\frac{1} {6} N k.
$$
D. $$
N k
$$
$$
\frac{1} {5} N k.
$$
E. $$
N k
$$
$$
\frac{9} {4} N k.
$$
F. $$
0 N k
$$
$$
\frac{7} {4} N k.
$$
G. $$
N k
$$
$$
\frac{5} {4} N k.
$$
H. $$
3 N k
$$
$$
\frac{2} {3} N k.
$$
I. $$
N k
$$
$$
\frac{1} {2} N k.
$$
J. $$
N k
$$
$$
\frac{3} {4} N k.
$$
Answer: J
A solid contains $N$ non-interacting particles, each with a spin quantum number of 1. Each particle has three quantum states with quantum numbers $m=-1, 0, 1$. In the solid, particles in the quantum states $m=1$ and $m=-1$ have the same energy $\varepsilon$, where $\varepsilon > 0$, while particles in the state $m=0$ have zero energy.
(1) What is the functional relationship between entropy $S$ and temperature $T$ ?
(2) What is the expression for heat capacity in the high-temperature limit $\varepsilon/kT \ll 1$ ?

Options:
A. $$
N k \mathrm{l n} \Big[ 1+\mathrm{e x p} \Big(-\frac{\varepsilon} {3 k T} \Big) \Big]+\frac{2 N \varepsilon} {T} \Big[ 3+\mathrm{e x p} \Big( \frac{\varepsilon} {k T} \Big) \Big]^{-1}
$$
$$
\frac{N k} {12} \left( {\frac{\varepsilon} {k T}} \right)^{2}
$$
B. $$
N k \mathrm{l n} \Big[ 3+\mathrm{e x p} \Big(-\frac{\varepsilon} {k T} \Big) \Big]+\frac{2 N \varepsilon} {T} \Big[ 1+\mathrm{e x p} \Big( \frac{\varepsilon} {k T} \Big) \Big]^{-1}
$$
$$
\frac{ N k} {3} \left( {\frac{\varepsilon} {k T}} \right)^{2}
$$
C. $$
N k \mathrm{l n} \Big[ 2+2 \mathrm{e x p} \Big(-\frac{\varepsilon} {k T} \Big) \Big]+\frac{3 N \varepsilon} {2 T} \Big[ 1+\mathrm{e x p} \Big( \frac{\varepsilon} {k T} \Big) \Big]^{-1}
$$
$$
\frac{N k} {4} \left( {\frac{\varepsilon} {k T}} \right)^{2}
$$
D. $$
N k \mathrm{l n} \Big[ 3+2 \mathrm{e x p} \Big(-\frac{\varepsilon} {k T} \Big) \Big]+\frac{N \varepsilon} {2 T} \Big[ 2+\mathrm{e x p} \Big( \frac{2 \varepsilon} {k T} \Big) \Big]^{-1}
$$
$$
\frac{3 N k} {10} \left( {\frac{\varepsilon} {k T}} \right)^{2}
$$
E. $$
N k \mathrm{l n} \Big[ 2+\mathrm{e x p} \Big(-\frac{3 \varepsilon} {k T} \Big) \Big]+\frac{N \varepsilon} {T} \Big[ 2+\mathrm{e x p} \Big( \frac{\varepsilon} {k T} \Big) \Big]^{-1}
$$
$$
\frac{3 N k} {6} \left( {\frac{\varepsilon} {k T}} \right)^{2}
$$
F. $$
S = N k \mathrm{l n} \Big[ 1+2 \mathrm{e x p} \Big(-\frac{\varepsilon} {k T} \Big) \Big]+\frac{2 N \varepsilon} {T} \Big[ 2+\mathrm{e x p} \Big( \frac{\varepsilon} {k T} \Big) \Big]^{-1}
$$
$$
c \approx \frac{2 N k} {9} \left( {\frac{\varepsilon} {k T}} \right)^{2}
$$
G. $$
N k \mathrm{l n} \Big[ 1+\mathrm{e x p} \Big(-\frac{\varepsilon} {2 k T} \Big) \Big]+\frac{2 N \varepsilon} {3 T} \Big[ 2+\mathrm{e x p} \Big( \frac{2 \varepsilon} {k T} \Big) \Big]^{-1}
$$
$$
\frac{N k} {8} \left( {\frac{\varepsilon} {k T}} \right)^{2}
$$
H. $$
2 N k \mathrm{l n} \Big[ 1+\mathrm{e x p} \Big(-\frac{2 \varepsilon} {k T} \Big) \Big]+\frac{3 N \varepsilon} {T} \Big[ 1+\mathrm{e x p} \Big( \frac{\varepsilon} {k T} \Big) \Big]^{-1}
$$
$$
\frac{N k} {5} \left( {\frac{\varepsilon} {k T}} \right)^{2}
$$
I. $$
N k \mathrm{l n} \Big[ 2+3 \mathrm{e x p} \Big(-\frac{\varepsilon} {k T} \Big) \Big]+\frac{N \varepsilon} {T} \Big[ 3+\mathrm{e x p} \Big( \frac{\varepsilon} {k T} \Big) \Big]^{-1}
$$
$$
\frac{2 N k} {7} \left( {\frac{\varepsilon} {k T}} \right)^{2}
$$
J. $$
N k \mathrm{l n} \Big[ 1+3 \mathrm{e x p} \Big(-\frac{2 \varepsilon} {k T} \Big) \Big]+\frac{N \varepsilon} {T} \Big[ 3+\mathrm{e x p} \Big( \frac{\varepsilon} {2 k T} \Big) \Big]^{-1}
$$
$$
\frac{N k} {11} \left( {\frac{\varepsilon} {k T}} \right)^{2}
$$
Answer: F
A cylindrical container with a height of $L$ and a cross-sectional area of $A$ is filled with a classical ideal gas, with each molecule having a mass of $m$. Due to the influence of the gravitational field, the gravitational acceleration is a constant $g$. Assuming the system is in thermal equilibrium, determine the average isochoric heat capacity per molecule, and examine the limiting behavior of the result as $T \to 0 \mathrm{K}$ and $T \to \infty$.

Options:
A. $$
\left\{\begin{aligned} {{}} & {{} {{} {} {} {\frac{2} {2} k, T \to0 K}}} \\ {{}} & {{} {{} {} {} {} {} {\frac{6} {2} k, T \to\infty}}} \\ \end{aligned} \right.
$$
B. $$
\left\{\begin{aligned} {{}} & {{} {{} {} {} {\frac{1} {2} k, T \to0 K}}} \\ {{}} & {{} {{} {} {} {} {} {\frac{2} {2} k, T \to\infty}}} \\ \end{aligned} \right.
$$
C. $$
\left\{\begin{aligned} {{}} & {{} {{} {} {} {\frac{8} {2} k, T \to0 K}}} \\ {{}} & {{} {{} {} {} {} {} {\frac{3} {2} k, T \to\infty}}} \\ \end{aligned} \right.
$$
D. $$
\left\{\begin{aligned} {{}} & {{} {{} {} {} {\frac{7} {2} k, T \to0 K}}} \\ {{}} & {{} {{} {} {} {} {} {\frac{1} {2} k, T \to\infty}}} \\ \end{aligned} \right.
$$
E. $$
\left\{\begin{aligned} {{}} & {{} {{} {} {} {\frac{9} {2} k, T \to0 K}}} \\ {{}} & {{} {{} {} {} {} {} {\frac{4} {2} k, T \to\infty}}} \\ \end{aligned} \right.
$$
F. $$
\left\{\begin{aligned} {{}} & {{} {{} {} {} {\frac{5} {2} k, T \to0 K}}} \\ {{}} & {{} {{} {} {} {} {} {\frac{3} {2} k, T \to\infty}}} \\ \end{aligned} \right.
$$
G. $$
\left\{\begin{aligned} {{}} & {{} {{} {} {} {\frac{3} {2} k, T \to0 K}}} \\ {{}} & {{} {{} {} {} {} {} {\frac{5} {2} k, T \to\infty}}} \\ \end{aligned} \right.
$$
H. $$
\left\{\begin{aligned} {{}} & {{} {{} {} {} {\frac{6} {2} k, T \to0 K}}} \\ {{}} & {{} {{} {} {} {} {} {\frac{4} {2} k, T \to\infty}}} \\ \end{aligned} \right.
$$
I. $$
\left\{\begin{aligned} {{}} & {{} {{} {} {} {\frac{4} {2} k, T \to0 K}}} \\ {{}} & {{} {{} {} {} {} {} {\frac{2} {2} k, T \to\infty}}} \\ \end{aligned} \right.
$$
J. $$
\left\{\begin{aligned} {{}} & {{} {{} {} {} {\frac{5} {2} k, T \to0 K}}} \\ {{}} & {{} {{} {} {} {} {} {\frac{5} {2} k, T \to\infty}}} \\ \end{aligned} \right.
$$
Answer: F
Certain imported equipment should be subject to consumption tax, with the calculation formula being ().

Options:
A. Taxable consumption tax amount = $\text{Customs duty} + \text{CIF price} \times \text{consumption tax rate}$
B. Taxable consumption tax amount = $\text{CIF price} \div \text{customs duty} \times \text{consumption tax}$
C. Taxable consumption tax amount = $\text{CIF price} + \text{customs duty} - \text{consumption tax rate}$
D. Taxable consumption tax amount = $\text{Customs duty} + \text{CIF price} \times \text{customs tax rate}$
E. Taxable consumption tax amount = $\frac{\text{CIF price} + \text{customs duty}}{1 - \text{consumption tax rate}} \times \text{consumption tax rate}$
F. Taxable consumption tax amount = $\frac{\text{CIF price} \times \text{customs duty}}{1 + \text{consumption tax rate}}$
G. Taxable consumption tax amount = $\text{CIF price} \times (\text{consumption tax rate} + \text{customs duty})$
H. Taxable consumption tax amount = $\text{CIF price} \times \text{customs duty rate} - \text{consumption tax rate}$
I. Taxable consumption tax amount = $\text{Customs duty} \div \text{CIF price} \times \text{consumption tax rate}$
J. Taxable consumption tax amount = $\frac{\text{CIF price} \times \text{customs duty}}{\text{consumption tax rate}}$
Answer: E
Conduct an elevation survey at a construction site. Point M is a benchmark with a known elevation of 12.000m; Point $\mathrm{N}$ is the point to be measured. Set up the level between M and N, first place the staff at point $\mathbf{M}$, and read the backsight reading as 4.500m, then place the staff at point $\mathrm{N}$ and read the foresight reading as 3.500m. The elevation of point $\mathrm{N}$ is ()m.

Options:
A. 13.000
B. 13.500
C. 12.500
D. 14.000
E. 11.000
F. 11.500
G. 12.000
H. 10.000
I. 15.000
J. 10.500
Answer: A
A reinforced concrete beam with a span of 8m, when there are no specific design requirements, should have a concrete strength at the time of removing the bottom formwork and support that is greater than or equal to the standard value of the design concrete cube compressive strength ().

Options:
A. $55\%$
B. $85\%$
C. $95\%$
D. $70\%$
E. $75\%$
F. $65\%$
G. $60\%$
H. $90\%$
I. $50\%$
J. $40\%$
Answer: E
Given that the discharge voltage of a certain sphere gap under standard atmospheric conditions is $U_{0}=1000 \mathrm{kV}$, what is the discharge voltage of this sphere gap when $T=28^{\circ} \mathrm{C}$ and $P=100 \mathrm{kPa}$?

Options:
A. $$
1 0 0 4 \mathrm{k V}
$$
B. $$
9 6 1 \mathrm{k V}
$$
C. $$
1 0 5 6 \mathrm{k V}
$$
D. $$
9 8 2 \mathrm{k V}
$$
E. $$
8 5 9 \mathrm{k V}
$$
F. $$
7 9 3 \mathrm{k V}
$$
G. $$
9 5 0 \mathrm{k V}
$$
H. $$
9 2 3 \mathrm{k V}
$$
I. $$
8 0 7 \mathrm{k V}
$$
J. $$
1 1 2 0 \mathrm{k V}
$$
Answer: B
A capacitor has a capacitance of $C {=} 2000 \mathrm{pF,} \ \ \mathrm{tan} \delta{=} 0.01$, and the insulation resistance under direct current is 2000 MΩ. What is the ratio of the equivalent resistance in the parallel equivalent circuit of dielectric loss under alternating current to the direct current insulation resistance?

Options:
A. $$0.0572$$
B. $$0.0826$$
C. $$0.0734$$
D. $$0.0763$$
E. $$0.0795$$
F. $$0.0948$$
G. $$0.0617$$
H. $$0.0659$$
I. $$0.0875$$
J. $$0.0893$$
Answer: E
A flask with a stopper, with a volume of $2.0 \times 10^{-3} \mathrm{~m}^{3}$, contains oxygen at 0.1 MPa and 300 K. When the system is heated to 400 K, the stopper pops open, and it is immediately closed again and heating is stopped. The flask gradually cools back down to 300 $\mathbf{K}$. Assuming the external gas pressure is always 0.1 MPa, what is the remaining mass of oxygen in the flask?

Options:
A. 0.0121kg
B. 0.0028kg
C. 0.0019kg
D. 0.0032kg
E. 0.0030kg
F. 0.0013kg
G. 0.00101kg
H. 0.0012kg
I. 0.0025kg
J. 0.0008kg
Answer: C
A clean tungsten wire is placed in oxygen at a pressure of $1.33 \times 10^{-2} \mathrm{Pa}$ and a temperature of 300°C. Assuming that the adsorbed oxygen molecules are arranged in close-packed formation, how long does it take to form a single monolayer?

Options:
A. 0.86s
B. 0.66s
C. 0.36s
D. 0.96s
E. 0.76s
F. 0.46s
G. 0.26s
H. 0.06s
I. 0.56s
J. 0.16s
Answer: H
A thin metal wire vertically suspends a uniform disk with mass $m$ and radius $R$ along its central axis. The disk can rotate freely around the axis, with its surface parallel to a horizontal plate. The space between the disk and the plate is filled with a fluid of viscosity $\eta$. Initially, the disk rotates with an angular velocity of $\omega_{0}$. The distance between the disk's surface and the large plate is $d$, and the velocity gradient of the fluid is uniform along any vertical line directly below the disk. What is the angular velocity of the disk at time $t$ ?

Options:
A. $$
\omega_{0} \, \cdot\, \operatorname{e x p} \! \Big({\frac{-\eta\, \pi R^{t} t} {m d}} \! \Big)
$$
B. $$
\omega_{0} \, \cdot\, \operatorname{e x p} \! \Big(-{\frac{2\eta\, \pi t} {m R d}} \! \Big)
$$
C. $$
\omega_{0} \, \cdot\, \operatorname{e x p} \! \Big(-{\frac{\eta\, \pi R^{3} t} {2m d}} \! \Big)
$$
D. $$
\omega_{0} \, \cdot\, \operatorname{e x p} \! \Big(-{\frac{\eta\, t R^{2} \pi} {m d}} \! \Big)
$$
E. $$
\omega_{0} \, \cdot\, \operatorname{e x p} \! \Big(-{\frac{\eta\, \pi R t} {m d^{2}}} \! \Big)
$$
F. $$
\omega_{0} \, \cdot\, \operatorname{e x p} \! \Big(-{\frac{\eta\, \pi R^{2} t} {m d}} \! \Big)
$$
G. $$
\omega_{0} \, \cdot\, \operatorname{e x p} \! \Big(-{\frac{\eta^{2} \pi R^{2} t} {m d}} \! \Big)
$$
H. $$
\omega_{0} \, +\, \operatorname{e x p} \! \Big(-{\frac{\eta\, \pi R^{2} t} {m d}} \! \Big)
$$
I. $$
\omega_{0} \, \cdot\, \operatorname{e x p} \! \Big(-{\frac{\eta t \pi R^{2}} {2m d}} \! \Big)
$$
J. $$
\omega_{0} \, \cdot\, \operatorname{e x p} \! \Big(-{\frac{2\eta\, \pi R^{2} t} {m d^{2}}} \! \Big)
$$
Answer: F
A certain monoatomic gas has a molar mass of $M$, temperature $T$, and pressure $p$. It is known that the probability of a molecule being collided with during a distance $x$ (in meters) is $1-\frac{1}{\mathrm{e}^{2}}$. What is thermal conductivity of this gas ?
( assuming the molecules are rigid and the molecular diameter is $d$ )

Options:
A. $$
{\frac{1} {3}} x p \, \cdot\, C_{v, \, n} \cdot\, {\sqrt{\frac{2} {\pi R T M}}}
$$
B. $$
{\frac{1} {3}} x p \, \cdot\, C_{p, \, m} \cdot\, {\sqrt{\frac{R T M} {2 \pi}}}
$$
C. $$
{\frac{1} {4}} x p \, \cdot\, C_{v, \, m} \cdot\, {\sqrt{\frac{2 \pi R} {T M}}}
$$
D. $$
{\frac{1} {3}} x p \, \cdot\, C_{n, \, m} \cdot\, {\sqrt{\frac{2} {\pi R T M}}}
$$
E. $$
{\frac{1} {3}} x p \, \cdot\, C_{v, \, m} \cdot\, {\sqrt{\frac{\pi R T M} {2}}}
$$
F. $$
{\frac{1} {3}} x p \, \cdot\, C_{v, \, m} \cdot\, {\sqrt{\frac{R T} {2 \pi M}}}
$$
G. $$
{\frac{1} {3}} x p \, \cdot\, C_{v, \, m} \cdot\, {\sqrt{\frac{2 \pi} {R T M}}}
$$
H. $$
{\frac{2} {3}} x p \, \cdot\, C_{v, \, m} \cdot\, {\sqrt{\frac{2} {\pi R T M}}}
$$
I. $$
{\frac{1} {2}} x p \, \cdot\, C_{v, \, m} \cdot\, {\sqrt{\frac{2} {\pi R T M}}}
$$
J. $$
{\frac{1} {3}} x p \, \cdot\, C_{V, \, m} \cdot\, {\sqrt{\frac{2} {\pi R T M}}}
$$
Answer: J
In a spherical container with a radius of $R$ containing a certain ideal gas, the molecular number density is known to be $n$, and the mass of each molecule is $m$. The average value of the square of the molecular speed is given by $\overline{{{v^{2}}}}=\frac{1}{N} ( \, v_{1}^{2} \,+\, v_{2}^{2} \,+\, \cdots\,+\, v_{N}^{2} \, )=\sum_{i=1}^{N} \; ( \frac{v_{i}^{2}}{N})$, where $v_{i}$ is the speed of the $i$-th molecule, and $N=n \cdot{\frac{4}{3}} \pi R^{3}$ is the total number of molecules within the spherical container. Give the pressure $p$ exerted by the molecules on the walls of the container.

Options:
A. $$
{\frac{2} {3}} n m {\overline{v^{2}}}
$$
B. $$
{\frac{3} {2}} n R T
$$
C. $$
{\frac{1} {3}} n m {\stackrel{\_} {v^{2}}}
$$
D. $$
2 n m v_{\text{rms}}^{2}
$$
E. $$
n m v_{\text{rms}}^{2}
$$
F. $$
n R T
$$
G. $$
{\frac{1} {2}} n m {\stackrel{\_} {v^{2}}}
$$
H. $$
{\frac{1} {2}} n m v_{\text{avg}}^{2}
$$
I. $$
{\frac{3} {2}} n m {\stackrel{\_} {v^{2}}}
$$
J. $$
2 n m {\stackrel{\_} {v^{2}}}
$$
Answer: C
Each time the pump is used, it compresses air with an initial pressure $p_{0} = 1 \times 10^{5} \mathrm{~Pa}$, temperature $t_{0} = -3 \mathrm{°C}$, and volume $V_{0} = 4 \mathrm{~L}$ into the container. The container has a volume of $V = 1.5 \times 10^{3} \mathrm{~L}$. How many times must the air be pumped into the container until the temperature of the container, which was originally open to the air, rises to $45 \mathrm{°C}$ and the pressure increases to $p = 2 \times 10^{5} \mathrm{~Pa}$?

Options:
A. 306
B. 147
C. 192
D. 328
E. 175
F. 289
G. 262
H. 243
I. 304
J. 211
Answer: G
A mass-neutral spring hangs from the ceiling, with a length of 20 cm. A mass $M$ is attached to the lower end of the spring. When you hold the mass in your hand, the spring is exactly relaxed. Suddenly, you remove your hand, causing the mass $M$ to vibrate along with the spring. During the vibration, the lowest position of the mass is 10 cm below where you initially supported it. Question: What is the frequency of the system's vibration? What is the velocity of the mass when it is 5 cm below its initial resting position? If an additional weight of 300 g is added to the original mass, causing the vibration frequency to become half of the original frequency, what should $M$ be? Where is the new equilibrium position?

Options:
A. $\omega_{0} \ =\ 1 3 rad/s$, $u \ =\ 0$ 82 m/s; $M$ is 0.18 kg; originally 35 cm below the hand support position
B. $\omega_{0} \ =\ 1 5 rad/s$, $u \ =\ 0$ 79 m/s; $M$ is 0.25 kg; originally 10 cm below the hand support position
C. $\omega_{0} \ =\ 1 2 rad/s$, $u \ =\ 0$ 65 m/s; $M$ is 0.05 kg; originally 30 cm below the hand support position
D. $\omega_{0} \ =\ 1 4 rad/s$, $u \ =\ 0$ 71 m/s; $M$ is 0.1 kg; originally 20 cm below the hand support position
E. $\omega_{0} \ =\ 1 7 rad/s$, $u \ =\ 0$ 75 m/s; $M$ is 0.3 kg; originally 45 cm below the hand support position
F. $\omega_{0} \ =\ 1 8 rad/s$, $u \ =\ 0$ 52 m/s; $M$ is 0.2 kg; originally 15 cm below the hand support position
G. $\omega_{0} \ =\ 1 0 rad/s$, $u \ =\ 0$ 67 m/s; $M$ is 0.14 kg; originally 50 cm below the hand support position
H. $\omega_{0} \ =\ 1 9 rad/s$, $u \ =\ 0$ 55 m/s; $M$ is 0.12 kg; originally 40 cm below the hand support position
I. $\omega_{0} \ =\ 1 1 rad/s$, $u \ =\ 0$ 58 m/s; $M$ is 0.22 kg; originally 5 cm below the hand support position
J. $\omega_{0} \ =\ 1 6 rad/s$, $u \ =\ 0$ 68 m/s; $M$ is 0.15 kg; originally 25 cm below the hand support position
Answer: D
For a single-degree-of-freedom mechanical system subject to a sinusoidal excitation force of $10 \sin(0.1 \pi t) \ \mathrm{N}$, the steady-state displacement of the system is $0.1 \sin(0.1 \pi t - 30^{\circ}) \ \mathrm{m}$. Try to determine the work done by the excitation force over 1 minute and 1 second.

Options:
A. $$
4.85 \ \mathrm{J}, 0.065 \ \mathrm{J}_{\circ}
$$
B. $$
4.90 \ \mathrm{J}, 0.055 \ \mathrm{J}_{\circ}
$$
C. $$
4.75 \ \mathrm{J}, 0.047 \ \mathrm{J}_{\circ}
$$
D. $$
4.50 \ \mathrm{J}, 0.035 \ \mathrm{J}_{\circ}
$$
E. $$
4.80 \ \mathrm{J}, 0.060 \ \mathrm{J}_{\circ}
$$
F. $$
4.95 \ \mathrm{J}, 0.052 \ \mathrm{J}_{\circ}
$$
G. $$
4.71 \ \mathrm{J}, 0.045 \ \mathrm{J}_{\circ}
$$
H. $$
4.60 \ \mathrm{J}, 0.042 \ \mathrm{J}_{\circ}
$$
I. $$
5.00 \ \mathrm{J}, 0.050 \ \mathrm{J}_{\circ}
$$
J. $$
4.65 \ \mathrm{J}, 0.040 \ \mathrm{J}_{\circ}
$$
Answer: G
There is a thin steel membrane with a radius of $0.02 \ \mathrm{m}$ and a thickness of $10^{-4} \ \mathrm{m}$, with a tension on the membrane of $2.0 \times 10^{4} \ \mathrm{N/m}$. Determine: What is the second harmonic frequency of symmetric vibrations for the circular membrane? When the membrane vibrates at this frequency, what are the radii of the two nodal circles? (3) If the displacement amplitude at the center of the membrane is $1.0 \times 10^{-4} \ \mathrm{m}$ when vibrating at this frequency, what is the average displacement amplitude?

Options:
A. $$ f_{2} \,=\, 2 0. 9 6 \times1 0^{3} \ \mathrm{H z} ; 6. 5 5 \times1 0^{-4} \ \mathrm{m}, 2. 3 8 \times1 0^{-2} \ \mathrm{m} ; 7. 2 4 \times1 0^{-6} \ \mathrm{m} $$
B. $$ f_{2} \,=\, 1 8. 9 6 \times1 0^{3} \ \mathrm{H z} ; 5. 8 5 \times1 0^{-3} \ \mathrm{m}, 1. 0 8 \times1 0^{-2} \ \mathrm{m} ; 6. 3 4 \times1 0^{-6} \ \mathrm{m} $$
C. $$
f_{2} \,=\, 1 1. 9 6 \times1 0^{3} \ \mathrm{H z} ; 5. 5 5 \times1 0^{-3} \ \mathrm{m}, 1. 2 8 \times1 0^{-2} \ \mathrm{m} ; 6. 2 4 \times1 0^{-6} \ \mathrm{m}
$$
D. $$ f_{2} \,=\, 9 1. 9 6 \times1 0^{2} \ \mathrm{H z} ; 5. 3 5 \times1 0^{-3} \ \mathrm{m}, 1. 0 8 \times1 0^{-2} \ \mathrm{m} ; 6. 1 4 \times1 0^{-6} \ \mathrm{m} $$
E. $$ f_{2} \,=\, 1 0. 9 6 \times1 0^{3} \ \mathrm{H z} ; 5. 7 5 \times1 0^{-3} \ \mathrm{m}, 1. 3 8 \times1 0^{-2} \ \mathrm{m} ; 5. 2 4 \times1 0^{-6} \ \mathrm{m} $$
F. $$ f_{2} \,=\, 1 1. 6 6 \times1 0^{3} \ \mathrm{H z} ; 5. 9 5 \times1 0^{-3} \ \mathrm{m}, 1. 5 8 \times1 0^{-2} \ \mathrm{m} ; 5. 4 4 \times1 0^{-6} \ \mathrm{m} $$
G. $$ f_{2} \,=\, 1 3. 9 6 \times1 0^{3} \ \mathrm{H z} ; 5. 9 5 \times1 0^{-3} \ \mathrm{m}, 1. 4 8 \times1 0^{-2} \ \mathrm{m} ; 6. 6 4 \times1 0^{-6} \ \mathrm{m} $$
H. $$ f_{2} \,=\, 1 4. 9 6 \times1 0^{3} \ \mathrm{H z} ; 5. 0 5 \times1 0^{-3} \ \mathrm{m}, 1. 2 0 \times1 0^{-2} \ \mathrm{m} ; 5. 7 4 \times1 0^{-6} \ \mathrm{m} $$
I. $$ f_{2} \,=\, 1 2. 4 6 \times1 0^{3} \ \mathrm{H z} ; 5. 1 5 \times1 0^{-3} \ \mathrm{m}, 1. 6 8 \times1 0^{-2} \ \mathrm{m} ; 6. 5 4 \times1 0^{-6} \ \mathrm{m} $$
J. $$ f_{2} \,=\, 1 5. 9 6 \times1 0^{3} \ \mathrm{H z} ; 4. 5 5 \times1 0^{-3} \ \mathrm{m}, 1. 1 8 \times1 0^{-2} \ \mathrm{m} ; 5. 2 4 \times1 0^{-6} \ \mathrm{m} $$
Answer: C
The sound intensity level of plane sound waves in the air is 70 dB. Find the sound energy density and effective sound pressure; the sound pressure level of plane sound waves in water is 70 dB (reference value $1 \ \mu\mathrm{bar}$). Find its sound energy density and effective sound pressure.

Options:
A. $\stackrel{.} {E}_{a}=2.1 \times10^{-8} \mathrm{~ J / m^3, 0.62 ~ Pa} ; 4.9 \times10^{-4} \mathrm{~ J / m^3, 325 ~ Pa}$
B. $\stackrel{.} {E}_{a}=2.9 \times10^{-8} \mathrm{~ J / m^3, 0.64 ~ Pa} ; 4.6 \times10^{-4} \mathrm{~ J / m^3, 310 ~ Pa}$
C. $\stackrel{.} {E}_{a}=4.2 \times10^{-8} \mathrm{~ J / m^3, 0.80 ~ Pa} ; 3.5 \times10^{-4} \mathrm{~ J / m^3, 290 ~ Pa}$
D. $\stackrel{.} {E}_{a}=3.3 \times10^{-8} \mathrm{~ J / m^3, 0.70 ~ Pa} ; 4.1 \times10^{-4} \mathrm{~ J / m^3, 315 ~ Pa}$
E. $\stackrel{.} {E}_{a}=2.6 \times10^{-8} \mathrm{~ J / m^3, 0.66 ~ Pa} ; 4.7 \times10^{-4} \mathrm{~ J / m^3, 295 ~ Pa}$
F. $\stackrel{.} {E}_{a}=2.8 \times10^{-8} \mathrm{~ J / m^3, 0.90 ~ Pa} ; 4.3 \times10^{-4} \mathrm{~ J / m^3, 300 ~ Pa}$
G. $\stackrel{.} {E}_{a}=1.7 \times10^{-8} \mathrm{~ J / m^3, 0.75 ~ Pa} ; 5.1 \times10^{-4} \mathrm{~ J / m^3, 320 ~ Pa}$
H. $\stackrel{.} {E}_{a}=2.5 \times10^{-8} \mathrm{~ J / m^3, 0.60 ~ Pa} ; 4.8 \times10^{-4} \mathrm{~ J / m^3, 330 ~ Pa}$
I. $\stackrel{.} {E}_{a}=3.1 \times10^{-8} \mathrm{~ J / m^3, 0.68 ~ Pa} ; 4.0 \times10^{-4} \mathrm{~ J / m^3, 305 ~ Pa}$
J. $\stackrel{.} {E}_{a}=2.4 \times10^{-8} \mathrm{~ J / m^3, 0.72 ~ Pa} ; 3.8 \times10^{-4} \mathrm{~ J / m^3, 285 ~ Pa}$
Answer: B
A plane harmonic wave in the air is perpendicularly incident on a flat surface with a characteristic impedance of $785 \mathrm{~Rayl}$. What is the standing wave ratio? (The standing wave ratio is defined as the ratio of the maximum sound pressure to the minimum sound pressure in the standing wave field.)

Options:
A. $$
SWR=0.5
$$
B. $$
SWR=2.3
$$
C. $$
SWR=3.5
$$
D. $$
SWR=2.0
$$
E. $$
SWR=1.2
$$
F. $$
SWR=1.9
$$
G. $$
SWR=0.9
$$
H. $$
SWR=4.0
$$
I. $$
SWR=0.7
$$
J. $$
SWR=3.1
$$
Answer: F
An exponential horn has a throat radius of $a_{0}=2 \ \mathrm{cm}$. It is known that the cross-sectional area of the horn at a distance of 1m from the throat is 100 times the area of the throat. What should the flare constant of the horn be? What is the cutoff frequency of such a horn?

Options:
A. 5.2,133.0Hz
B. 4.5,126.7Hz
C. 4.4,120.0Hz
D. 5.0,128.5Hz
E. 4.7,129.1Hz
F. 4.9,132.4Hz
G. 4.8,130.2Hz
H. 4.2,127.3Hz
I. 5.1,124.9Hz
J. 4.6,125.8Hz
Answer: J
Given that the voice coil resistance of an electrically powered speaker is negligible, it is placed in a vacuum where the measured resonance frequency is $f_{a} = 110 \text{Hz}$, and the impedance at resonance is $Z_{a} = 10 \Omega$. If a mass of 10g is added to the voice coil and measurements are again taken in a vacuum, the resonance frequency changes to $f_{a}^{\prime} = 77 \text{Hz}$. Find the impedance at the resonance frequency $f_{a}^{\prime}$ after adding the mass, as well as the total mass and total mechanical compliance of the speaker's vibrating system.

Options:
A. 9 Ω;10g,2.3x10 $^{-4}$m/N
B. 7 Ω;10.1g,2.8x10 $^{-4}$m/N
C. 13 Ω;10g,2.5x10 $^{-4}$m/N
D. 14 Ω;9.8g,2.3x10 $^{-4}$m/N
E. 12 Ω;9.5g,2.4x10 $^{-4}$m/N
F. 11 Ω;8.9g,2.1x10 $^{-4}$m/N
G. 10 Ω;9.6g,2.2x10 $^{-4}$m/N
H. 8 Ω;9.2g,2.2x10 $^{-4}$m/N
I. 9 Ω;9.7g,2.6x10 $^{-4}$m/N
J. 15 Ω;9.9g,2.7x10 $^{-4}$m/N
Answer: G
A transducer uses a copper titanate bending bilayer crystal, with an equivalent circuit similar to Problem 3-55. Its component parameters are: $n=0.0068l/mt$, $C_{\mathrm{m}}=40.6 \times 10^{-12} l^{3}/wt^{3}$, $M_{\mathrm{m}}=1530lwt$; $C_{\mathrm{E}}=1.28 \times 10^{-8}lw/t$. Here, $l$, $w$, and $t$ represent the length, width, and thickness of the crystal, respectively. Given $\omega=1000\ \mathrm{s}^{-1}$, and a root-mean-square force of 0.01 N applied on a crystal with dimensions: length 10 cm, width 2.5 cm, and thickness 0.2 cm, find the open-circuit voltage generated by the transducer.

Options:
A. 0.35V
B. 0.05V
C. 0.70V
D. 0.30V
E. 0.25V
F. 0.45V
G. 0.60V
H. 0.50V
I. 0.10V
J. 0.15V
Answer: E
A sealed barium titanate ceramic cylinder with an outer diameter of 5 cm, an inner diameter of 4.5 cm, and a length of 10 cm, $K_{\mathrm{31}}$ 1 = 0.19, $s\frac{E}{11} = 8.6 \times 10^{-12}$ m$^{2}$/N, $\frac{\varepsilon33}{\varepsilon0}$ ≈ 1200. Try to calculate its low-frequency receiving sensitivity.

Options:
A. -100dB (reference value $\mathrm{1V / \mu bar}$)
B. -45dB (reference value $\mathrm{1V / \mu bar}$)
C. -55dB (reference value $\mathrm{1V / \mu bar}$)
D. -97dB (reference value $\mathrm{1V / \mu bar}$)
E. -60dB (reference value $\mathrm{1V / \mu bar}$)
F. -85dB (reference value $\mathrm{1V / \mu bar}$)
G. -70dB (reference value $\mathrm{1V / \mu bar}$)
H. -65dB (reference value $\mathrm{1V / \mu bar}$)
I. -80dB (reference value $\mathrm{1V / \mu bar}$)
J. -110dB (reference value $\mathrm{1V / \mu bar}$)
Answer: D
Assuming a seawater salinity of 35‰, the sound speed decreases uniformly from 1513 m/s at the sea surface to 1476 m/s at a depth of 10 m. Find: the sea surface temperature; the temperature gradient; the horizontal distance traveled by a horizontal sound ray reaching a depth of 10 m; the angle of depression of the sound ray at this point.

Options:
A. 15.9°C,-1.30°C/m,91.3m,11.5°
B. 16.8°C,-0.85°C/m,87.6m,13.2°
C. 17.3°C,-1.10°C/m,92.5m,11.9°
D. 16.5°C,-1.50°C/m,92.2m,13.1°
E. 17.8°C,-1.00°C/m,88.7m,12.0°
F. 18.1°C,-1.35°C/m,90.8m,12.3°
G. 15.5°C,-1.25°C/m,91.0m,12.6°
H. 18.5°C,-1.60°C/m,89.2m,13.5°
I. 17.1°C,-1.24°C/m,89.9m,12.7°
J. 18.0°C,-0.75°C/m,90.1m,11.8°
Answer: I
At a depth of 1500 meters, the salinity is 32‰ and the temperature is 1.2°C. Assuming the temperature and salinity remain constant, determine the speed of sound at this location, as well as the radius of the horizontal sound ray and the sound ray with an emission angle of 5°.

Options:
A. 1483.5m/s,89.5km,90.0km
B. 1488.2m/s,87.3km,88.0km
C. 1500.3m/s,85.7km,86.2km
D. 1475.4m/s,86.8km,87.1km
E. 1472.6m/s,85.9km,86.3km
F. 1480.1m/s,86.1km,86.8km
G. 1469.7m/s,84.5km,85.9km
H. 1492.5m/s,88.6km,89.3km
I. 1494.8m/s,89.0km,90.2km
J. 1473.9m/s,87.0km,87.5km
Answer: D
Using one pound of explosives as a sound source to detect a submarine in a direct lateral position. The background noise corresponds to the deep-sea environmental noise of a sea state level of 3. The receiving hydrophone is omnidirectional, operating at a frequency of 5 kHz with a bandwidth of 1 kHz. The mixed layer thickness is 100 feet, with both the sound source and receiver at a depth of 50 ft, and the target at a depth of 500 ft. Assuming a detection probability of 0.90, a false alarm probability of 0.01%, and an echo duration of 0.1 seconds, find the maximum detection range.

Options:
A. 8.2 x 10 $^{3}$yd.
B. 3.2 x 10 $^{3}$yd.
C. 3.7 x 10 $^{3}$yd.
D. 4.0 x 10 $^{3}$yd.
E. 4.5 x 10 $^{3}$yd.
F. 6.0 x 10 $^{3}$yd.
G. 7.5 x 10 $^{3}$yd.
H. 5.1 x 10 $^{3}$yd.
I. 2.8 x 10 $^{3}$yd.
J. 5.7 x 10 $^{3}$yd.
Answer: E
A simple method for measuring sound source radiation power under semi-anechoic chamber conditions refers to the national standard GB4214-84. On a hemispherical surface 1 meter away from the equivalent sound center of the motor, the broadband noise levels measured at the five evenly distributed area center points are: 69 dB, 73 dB, 70 dB, 72.5 dB, and 74 dB. The ambient broadband noise level is 62 dB. Determine the motor's radiated noise sound power level and sound power.

Options:
A. Sound power level 69.50 dB (reference value 1 pW), sound power 12.90 W
B. Sound power level 71.00 dB (reference value 1 pW), sound power 14.50 W
C. Sound power level 72.00 dB (reference value 1 pW), sound power 15.00 W
D. Sound power level 70.05 dB (reference value 1 pW), sound power 13.50 W
E. Sound power level 73.00 dB (reference value 1 pW), sound power 16.00 W
F. Sound power level 72.75 dB (reference value 1 pW), sound power 15.75 W
G. Sound power level 72.25 dB (reference value 1 pW), sound power 15.25 W
H. Sound power level 70.50 dB (reference value 1 pW), sound power 14.00 W
I. Sound power level 69.90 dB (reference value 1 pW), sound power 13.25 W
J. Sound power level 71.69 dB (reference value 1 pW), sound power 14.76 W
Answer: J
Given an indoor sound pressure level of 80 dB, how much energy passes through an open window with an area of 1 m$^{2}$ per unit time? What is the sound pressure level at a vertical distance of 20 m outside the window? At the same distance, what is the sound pressure level in the direction forming a 45° angle with the normal?

Options:
A. 3.0 x 10 $^{-5}$ J;42 dB;40.3 dB
B. 7.0 x 10 $^{-4}$ J;44 dB;42.1 dB
C. 1.0 x 10 $^{-4}$ J;43 dB;41.5 dB
D. 6.0 x 10 $^{-5}$ J;41 dB;40.5 dB
E. 8.0 x 10 $^{-7}$ J;39 dB;37.8 dB
F. 1.0 x 10 $^{-6}$ J;50 dB;43.3 dB
G. 5.0 x 10 $^{-3}$ J;49 dB;45.7 dB
H. 2.0 x 10 $^{-4}$ J;45 dB;41.2 dB
I. 9.0 x 10 $^{-6}$ J;47 dB;44.0 dB
J. 4.0 x 10 $^{-4}$ J;38 dB;39.0 dB
Answer: C
Design two experiments to detect signals in noise: one using a "Yes or No" method, and another using a 2AFC (two-alternative forced choice) method. Both experiments involve sampling the same noise and noisy signals. In the first experiment, when the detection probability $P(D) = 0.5$, the false alarm probability $P(FA) = 0.002$. Under the same $P(D)$, what is the expected $P(FA)$ in the second experiment?

Options:
A. 0.008
B. 0.04
C. 0.07
D. 0.001
E. 0.02
F. 0.05
G. 0.09
H. 0.03
I. 0.01
J. 0.06
Answer: H
A rigid wall tube with a radius of 0.1 m is filled with air, and one end is equipped with a plane piston source to generate plane sound waves propagating in the tube. The other end of the tube is sealed with a rigid cap. The frequency of the sound waves radiated by the piston source is 6 kHz. At a certain position in the tube, a sound pressure standing wave ratio (SWR) of 8 is measured. After moving 0.5 m towards the closed end, an SWR of 9 is recorded. Derive the expression for the sound absorption coefficient in terms of the standing wave ratio and distance, and simplify this expression when the absorption coefficient $\alpha \ll 1$. Based on the above measurements, calculate the corresponding value of the absorption coefficient. Considering only the viscous losses and thermal conduction losses of the tube, what is the value of the absorption coefficient?

Options:
A. $\alpha$ = $[(SWR)_1 - (SWR)_3]/[(SWR)_1(SWR)_3$ $\times\left( \begin{array} {c c c} {{( w_{1}}} & {{+}} & {{w_{2}}} \\ \end{array} \right) ]$; 1.97 × $10^{-2} \; \mathrm{Np/m}; 1.75 \times 10^{-2}$ Np/m.
B. $\alpha$ = $[(SWR)_2 - (SWR)_3]/[(SWR)_1(SWR)_3$ $\times\left( \begin{array} {c c c} {{( s_{1}}} & {{+}} & {{s_{2}}} \\ \end{array} \right) ]$; 3.49 × $10^{-2} \; \mathrm{Np/m}; 2.22 × 10^{-2}$ Np/m.
C. $\alpha$ = $[(SWR)_1 - (SWR)_2]/[(SWR)_1(SWR)_2$ $\times\left( \begin{array} {c c c} {{( x_{1}}} & {{-}} & {{x_{2}}} \\ \end{array} \right) ]$; 2.78 × $10^{-2} \; \mathrm{Np/m}; 1.55 \times 10^{-2}$ Np/m.
D. $\alpha$ = $[(SWR)_1 + (SWR)_3]/[(SWR)_1(SWR)_3$ $\times\left( \begin{array} {c c c} {{( v_{1}}} & {{-}} & {{v_{2}}} \\ \end{array} \right) ]$; 1.88 × $10^{-2} \; \mathrm{Np/m}; 2.33 × 10^{-2}$ Np/m.
E. $\alpha$ = $[(SWR)_2 + (SWR)_3]/[(SWR)_1(SWR)_2$ $\times\left( \begin{array} {c c c} {{( q_{1}}} & {{-}} & {{q_{2}}} \\ \end{array} \right) ]$; 2.69 × $10^{-2} \; \mathrm{Np/m}; 1.84 × 10^{-2}$ Np/m.
F. $\alpha$ = $[(SWR)_2 + (SWR)_3]/[(SWR)_2(SWR)_3$ $\times\left( \begin{array} {c c c} {{( y_{1}}} & {{+}} & {{y_{2}}} \\ \end{array} \right) ]$; 3.01 × $10^{-2} \; \mathrm{Np/m}; 2.44 \times 10^{-2}$ Np/m.
G. $\alpha$ = $[(SWR)_1 + (SWR)_2]/[(SWR)_1(SWR)_2$ $\times\left( \begin{array} {c c c} {{( z_{1}}} & {{-}} & {{z_{2}}} \\ \end{array} \right) ]$; 4.15 × $10^{-2} \; \mathrm{Np/m}; 2.58 \times 10^{-2}$ Np/m.
H. $\alpha$ = $[(SWR)_3 - (SWR)_2]/[(SWR)_3(SWR)_2$ $\times\left( \begin{array} {c c c} {{( t_{1}}} & {{+}} & {{t_{2}}} \\ \end{array} \right) ]$; 2.82 × $10^{-2} \; \mathrm{Np/m}; 3.05 × 10^{-2}$ Np/m.
I. $\alpha$ = $[(SWR)_1 + (SWR)_3]/[(SWR)_1(SWR)_2$ $\times\left( \begin{array} {c c c} {{( u_{1}}} & {{+}} & {{u_{2}}} \\ \end{array} \right) ]$; 2.91 × $10^{-2} \; \mathrm{Np/m}; 2.67 × 10^{-2}$ Np/m.
J. $\alpha$ = $[(SWR)_2 - (SWR)_3]/[(SWR)_2(SWR)_3$ $\times\left( \begin{array} {c c c} {{( r_{1}}} & {{-}} & {{r_{2}}} \\ \end{array} \right) ]$; 3.76 × $10^{-2} \; \mathrm{Np/m}; 1.92 × 10^{-2}$ Np/m.
Answer: C
The concentration of the total plasma bicarbonate pool (mainly $\mathrm{HCO_3^- + CO_2}$) is $2.52 \times 10^{-2} \, M$. When $10^{-2} \, M \, \mathrm{H^+}$ is added, assuming the generated $CO_2$ can be removed, what is its pH value?

Options:
A. 8.23
B. 8.47
C. 9.55
D. 7.91
E. 9.01
F. 7.16
G. 6.84
H. 6.12
I. 7.61
J. 8.72
Answer: F
A plant grows in an atmosphere containing $\mathrm{^{14}C O_{2} ~ ( 3 \times~ 10^8 }$ counts per minute $/ \mu$ mol). Several weeks later, leaf extracts were prepared to determine glucose-1-phosphate using the isotope dilution method. To the 20 ml extract, 1.5 mmol of unlabeled glucose-1-phosphate dipotassium was added. A small amount of glucose-1-phosphate dipotassium was repeatedly isolated from the extract and recrystallized with an ethanol-water solution to a constant specific radioactivity. The specific radioactivity of the recrystallized salt is $2.6 \times 10^{5}$ counts per minute $/ \mu \mathrm{mol}$. Calculate the concentration of labeled glucose-1-phosphate in the extract is.

Options:
A. $$
6. 3 9 2 \times1 0^{-5} \mathrm{m o l}
$$
B. $$
5. 4 7 6 \times1 0^{-5} \mathrm{m o l}
$$
C. $$
3. 5 3 8 \times1 0^{-5} \mathrm{m o l}
$$
D. $$
1. 0 8 4 \times1 0^{-5} \mathrm{m o l}
$$
E. $$
4. 0 6 7 \times1 0^{-5} \mathrm{m o l}
$$
F. $$
0. 9 4 8 \times1 0^{-5} \mathrm{m o l}
$$
G. $$
9. 2 5 1 \times1 0^{-5} \mathrm{m o l}
$$
H. $$
2. 7 8 5 \times1 0^{-5} \mathrm{m o l}
$$
I. $$
7. 1 2 9 \times1 0^{-5} \mathrm{m o l}
$$
J. $$
8. 0 3 1 \times1 0^{-5} \mathrm{m o l}
$$
Answer: D
Assume each tube is inoculated with approximately 50 bacterial cells for 200 tubes, and then cultured until each tube contains millions of cells. One hundred of these cultures are individually placed onto plates with $\mathbf{T}_{1}$ bacteriophage. The other hundred cultures are placed onto plates with $\mathbf{T}_{4}$ bacteriophage. After overnight incubation, 95 of the $\mathbf{T}_{1}$ plates and 5 of the $\mathbf{T}_{4}$ plates have some colonies. By how many times is the mutation rate for $\mathbf{T}_{1}$ resistance greater than that for $\mathbf{T}_{4}$ resistance?

Options:
A. $$
\approx2 3
$$
B. $$
\approx1 5
$$
C. $$
\approx8 2
$$
D. $$
\approx6 0
$$
E. $$
\approx4 0
$$
F. $$
\approx9 5
$$
G. $$
\approx5 0
$$
H. $$
\approx7 5
$$
I. $$
\approx2 5
$$
J. $$
\approx3 0
$$
Answer: D
At 21°C and 37°C, $V_{m}$ is $140 \mathrm{n}M \times1^{-1} \times \text{min}^{-1}$ and $400 \mathbf{n}M \times\mathbf{l}^{-1} \times\mathcal{\text{min}}^{-1}$, respectively. Calculate the activation energy and the temperature coefficient $Q_{10}$ between 25°C and 35°C.

Options:
A. 11.600 cal/mol, 2.00
B. 11.900 cal/mol, 1.75
C. 10.200 cal/mol, 2.15
D. 12.300 cal/mol, 2.10
E. 12.050 cal/mol, 1.87
F. 10.800 cal/mol, 1.98
G. 12.500 cal/mol, 1.85
H. 11.828 cal/mol, 1.92
I. 13.450 cal/mol, 1.80
J. 11.700 cal/mol, 2.05
Answer: H
The crude preparation of a certain enzyme, after initial purification, contains protein at $2mg$ per ml. Take $0.1ul$ of this enzyme solution and catalyze the substrate in a total volume of $0.5ml$ for a reaction, producing $20nM$ of product after 2 minutes (under optimal reaction conditions). Calculate the concentration of this enzyme preparation.

Options:
A. $$
75 units/ml
$$
B. $$
100 units/ml
$$
C. $$
300 units/ml
$$
D. $$
150 units/ml
$$
E. $$
10 units/ml
$$
F. $$
500 units/ml
$$
G. $$
25 units/ml
$$
H. $$
200 units/ml
$$
I. $$
400 units/ml
$$
J. $$
50 units/ml
$$
Answer: B
Lead poisoning increases the daily excretion of fecal porphyrin, which can be measured by fluorescence in urine ($405nm$ excitation, $595nm$ emission). Properly process a $0.5ml$ urine sample from a person suspected of lead poisoning, diluting it to $25ml$ for fluorescence measurement. The following data were obtained: $I_{u} = 40$, $I_{b} = 5$, $I_{s} = 80$. The internal standard involves adding $1.25\mu g$ of porphyrin to a $25ml$ analysis sample volume. The total volume of urine excreted every 24 hours is $800ml$. What is the patient's daily porphyrin excretion? (The normal value is $75-300\mu g/$day.) Remember, $I_{u}$ refers to fluorescence from unknown plus blank; $I_{s}$ refers to fluorescence from internal standard plus unknown and blank.

Options:
A. $$
2 2 5 0 \ \mu\mathrm{g} / 2 4 \ \text{hours}
$$
B. $$
2 0 5 0 \ \mu\mathrm{g} / 2 4 \ \text{hours}
$$
C. $$
1 4 0 0 \ \mu\mathrm{g} / 2 4 \ \text{hours}
$$
D. $$
2 0 0 0 \ \mu\mathrm{g} / 2 4 \ \text{hours}
$$
E. $$
1 7 5 0 \ \mu\mathrm{g} / 2 4 \ \text{hours}
$$
F. $$
1 5 5 0 \ \mu\mathrm{g} / 2 4 \ \text{hours}
$$
G. $$
2 5 0 0 \ \mu\mathrm{g} / 2 4 \ \text{hours}
$$
H. $$
1 8 5 0 \ \mu\mathrm{g} / 2 4 \ \text{hours}
$$
I. $$
1 9 5 0 \ \mu\mathrm{g} / 2 4 \ \text{hours}
$$
J. $$
1 6 0 0 \ \mu\mathrm{g} / 2 4 \ \text{hours}
$$
Answer: E
The specific absorption coefficient ($a^{1cm}_{1\%}$) of the glycogen-iodine complex at $450nm$ is 0.20. Given an absorbance of 0.38 in an absorption cell with a thickness of $3cm$, calculate the concentration of glycogen in the solution.

Options:
A. $$0.663\%$$
B. $$0.702\%$$
C. $$0.455\%$$
D. $$0.623\%$$
E. $$0.819\%$$
F. $$0.580\%$$
G. $$0.699\%$$
H. $$0.511\%$$
I. $$0.732\%$$
J. $$0.590\%$$
Answer: A
The spaceship is moving away from the earth at a speed of $v = 0.8c$. When it is measured to be $6.66 \times 10^{8} \mathrm{km}$ from the earth in the earth's reference frame, a radio signal is sent from an observer on the earth to the spaceship. How long does it take for the signal to reach the spaceship in the spaceship's reference frame?

Options:
A. $$
8. 2 \times1 0^{3} ( \mathrm{s} )
$$
B. $$
7. 9 \times1 0^{3} ( \mathrm{s} )
$$
C. $$
3. 7 \times1 0^{3} ( \mathrm{s} )
$$
D. $$
2. 8 \times1 0^{3} ( \mathrm{s} )
$$
E. $$
6. 4 \times1 0^{3} ( \mathrm{s} )
$$
F. $$
9. 1 \times1 0^{3} ( \mathrm{s} )
$$
G. $$
1. 0 \times1 0^{4} ( \mathrm{s} )
$$
H. $$
3. 3 \times1 0^{3} ( \mathrm{s} )
$$
I. $$
5. 6 \times1 0^{3} ( \mathrm{s} )
$$
J. $$
4. 5 \times1 0^{3} ( \mathrm{s} )
$$
Answer: C
Two particles, each with a rest mass of $m$, are moving in the same direction with momenta of $5 m c$ and $10 m c$ respectively. What is the speed of the faster particle as observed from the slower one? And vice versa?

Options:
A. 0.571c
-0.571c
B. 0.782c
-0.782c
C. 0.729c
-0.729c
D. 0.548c
-0.548c
E. 0.593c
-0.593c
F. 0.851c
-0.851c
G. 0.643c
-0.643c
H. 0.673c
-0.673c
I. 0.465c
-0.465c
J. 0.612c
-0.612c
Answer: E
A $\pi^{+}$ meson with a rest energy of $140 \mathrm{MeV}$ is produced at an altitude of $100 \mathrm{km}$ in the earth's atmosphere. This $\pi^{+}$ meson has a total energy $E = 1.5 \times 10^{5} \mathrm{MeV}$ and moves vertically downward. In its own reference frame, it decays $2.0 \times 10^{-8} \mathrm{s}$ after being produced. At what altitude above sea level does it decay?

Options:
A. $$
1 0 3. 5 ( \mathrm{k m} )
$$
B. $$
9 3. 6 ( \mathrm{k m} )
$$
C. $$
8 0. 4 ( \mathrm{k m} )
$$
D. $$
7 5. 1 ( \mathrm{k m} )
$$
E. $$
1 5 0. 2 ( \mathrm{k m} )
$$
F. $$
1 4 5. 8 ( \mathrm{k m} )
$$
G. $$
1 2 5. 9 ( \mathrm{k m} )
$$
H. $$
1 2 0. 7 ( \mathrm{k m} )
$$
I. $$
1 6 0. 3 ( \mathrm{k m} )
$$
J. $$
1 8 5. 6 ( \mathrm{k m} )
$$
Answer: B
When an astronaut switches on a regular flashlight and throws it into space (with the flashlight steadily rotating around its axis), the question arises: what additional velocity does this "photon rocket" gain when the battery runs out two hours later?
Assume that the flashlight's bulb is located at the focal point of the projection surface, causing the emitted photons to be almost parallel to the flashlight's axis.

Options:
A. $$
6 \times1 0^{-4} ( \mathrm{m / s} )
$$
B. $$
4 \times1 0^{-5} ( \mathrm{m / s} )
$$
C. $$
3 \times1 0^{-6} ( \mathrm{m / s} )
$$
D. $$
9 \times1 0^{-7} ( \mathrm{m / s} )
$$
E. $$
1 \times1 0^{-3} ( \mathrm{m / s} )
$$
F. $$
2 \times1 0^{-4} ( \mathrm{m / s} )
$$
G. $$
8 \times1 0^{-5} ( \mathrm{m / s} )
$$
H. $$
7 \times1 0^{-6} ( \mathrm{m / s} )
$$
I. $$
5 \times1 0^{-5} ( \mathrm{m / s} )
$$
J. $$
1 \times1 0^{-2} ( \mathrm{m / s} )
$$
Answer: G
A photon collides with a stationary target proton, resulting in the following reaction.
$$
\gamma+\mathrm{p} \to\mathrm{p}+\psi^{\prime}
$$
The rest mass of the $\psi^{\prime}$ particle is approximately $4 m_{\mathrm{p}}$, where $m_{\mathrm{p}}$ is the rest mass of the proton. In the laboratory reference frame, what is the minimum energy $E_{0}$ that the photon must have to produce the above reaction ? (expressed in units of $m_{\mathrm{p}} c^{2}$)

Options:
A. $$
1 0 m_{\mathrm{p}} c^{2}
$$
B. $$
6 m_{\mathrm{p}} c^{2}
$$
C. $$
5 m_{\mathrm{p}} c^{2}
$$
D. $$
1 5 m_{\mathrm{p}} c^{2}
$$
E. $$
9 m_{\mathrm{p}} c^{2}
$$
F. $$
8 m_{\mathrm{p}} c^{2}
$$
G. $$
1 2 m_{\mathrm{p}} c^{2}
$$
H. $$
2 0 m_{\mathrm{p}} c^{2}
$$
I. $$
4 m_{\mathrm{p}} c^{2}
$$
J. $$
3 m_{\mathrm{p}} c^{2}
$$
Answer: G
The linear accelerator built at SLAC can produce electron and positron beams for collision experiments, with the electron energy in the laboratory being $50 \mathrm{GeV}$. Each beam contains $10^{10}$ particles and can be considered as a uniformly charged cylinder with a radius of $1.0 \mu\mathrm{m}$ and a length of 2.0 mm in the laboratory. For an observer moving with the same particle beam, what are its radius and length, respectively?

Options:
A. $$
2. 0 \mathrm{\,\mu m}
$$
$$
5 0 ( \mathrm{\,nm} )
$$
B. $$
1. 2 \mathrm{\,mm}
$$
$$
5 0 ( \mathrm{\,nm} )
$$
C. $$
0. 5 \mathrm{\,mm}
$$
$$
2 5 ( \mathrm{\,nm} )
$$
D. $$
1. 0 \mu\mathrm{m}
$$
$$
1 0 ( \mathrm{n m} )
$$
E. $$
1. 5 \mathrm{\,mm}
$$
$$
1 5 ( \mathrm{\,nm} )
$$
F. $$
1. 0 \mathrm{\,cm}
$$
$$
1 0 ( \mathrm{\,cm} )
$$
G. $$
0. 9 \mathrm{\,mm}
$$
$$
2 0 ( \mathrm{\,nm} )
$$
H. $$
0. 8 \mathrm{\,nm}
$$
$$
3 0 ( \mathrm{\,nm} )
$$
I. $$
3. 0 \mathrm{\,\mu m}
$$
$$
1 5 ( \mathrm{\,nm} )
$$
J. $$
1. 0 \mathrm{\,nm}
$$
$$
2 0 ( \mathrm{\,nm} )
$$
Answer: D
A relativistic particle with a rest mass of $m_{0}$ and kinetic energy of $2 m_{0}$ collides with another particle with a rest mass of $2 m_{0}$, and they combine to form a new particle. What is the rest mass of the composite particle ?

Options:
A. $$
{\sqrt{2 5}} m_{0}
$$
B. $$
{\sqrt{1 7}} m_{0}
$$
C. $$
{\sqrt{1 5}} m_{0}
$$
D. $$
{\sqrt{2 8}} m_{0}
$$
E. $$
{\sqrt{1 3}} m_{0}
$$
F. $$
{\sqrt{2 2}} m_{0}
$$
G. $$
{\sqrt{5 1}} m_{0}
$$
H. $$
{\sqrt{4 9}} m_{0}
$$
I. $$
{\sqrt{3 6}} m_{0}
$$
J. $$
{\sqrt{3 8}} m_{0}
$$
Answer: B
What is the threshold energy for a gamma ($\gamma$) ray to produce an electron-positron pair when interacting with a stationary electron ?

Options:
A. $$
\approx1. 6 2 1 \mathrm{M e V}
$$
B. $$
\approx3. 1 8 9 \mathrm{M e V}
$$
C. $$
\approx2. 8 4 7 \mathrm{M e V}
$$
D. $$
\approx1. 5 5 3 \mathrm{M e V}
$$
E. $$
\approx0. 9 7 5 \mathrm{M e V}
$$
F. $$
\approx3. 5 2 3 \mathrm{M e V}
$$
G. $$
\approx2. 7 5 6 \mathrm{M e V}
$$
H. $$
\approx2. 3 7 1 \mathrm{M e V}
$$
I. $$
\approx1. 9 6 8 \mathrm{M e V}
$$
J. $$
\approx2. 0 4 4 \mathrm{M e V}
$$
Answer: J
In the experiment, a $D^{0}$ meson with an energy of $18.6 \mathrm{GeV}$ was discovered using a bubble chamber. Its mass is $1.86 \mathrm{GeV}$, with an average lifetime of $\tau_{0} = 5 \times 10^{-13} \mathrm{s}$. It decays in the following manner: $\mathrm{D}^{0} \to \mathrm{K}^{+} + \pi$. To observe more than 50% of the decays, what is the required resolution of the bubble chamber ?

Options:
A. Close to 12mm
B. Nearly 9mm
C. Greater than 8mm
D. About 7mm
E. Around 15mm
F. More than 10mm
G. Approximately 5mm
H. Roughly 11mm
I. Less than 1mm
J. Just above 6mm
Answer: I