MikaStars39/nano-eval huggingface dataset:
A cylindrical resonant cavity made of copper with a diameter $D=3 \ \mathrm{cm}$ and a length $l=3$ cm is filled with a lossy dielectric material $\varepsilon_{\mathrm{ed}} \,=\, \varepsilon_{0} \, (2.5 \,-$ j0.0002). Calculate the resonant frequency and quality factor of the cavity when it is operating in the lowest oscillation mode.

Options:
A. $$
6. 4 2 \times1 0^{9} \mathrm{~ H z}
$$
$$
Q_{0 1}
\approx1 \ 1 3 0
$$
B. $$
4. 2 7 \times1 0^{9} \mathrm{~ H z}
$$
$$
Q_{0 1}
\approx2 \ 8 5 0
$$
C. $$
5. 7 1 \times1 0^{9} \mathrm{~ H z}
$$
$$
Q_{0 1}
\approx2 \ 4 5 0
$$
D. $$
6. 9 8 \times1 0^{9} \mathrm{~ H z}
$$
$$
Q_{0 1}
\approx1 \ 0 2 0
$$
E. $$
4. 8 3 \times1 0^{9} \mathrm{~ H z}
$$
$$
Q_{0 1}
\approx3 \ 3 9 0
$$
F. $$
7. 1 2 \times1 0^{9} \mathrm{~ H z}
$$
$$
Q_{0 1}
\approx4 \ 1 5 0
$$
G. $$
3. 2 6 \times1 0^{9} \mathrm{~ H z}
$$
$$
Q_{0 1}
\approx1 \ 4 9 0
$$
H. $$
5. 0 4 \times1 0^{9} \mathrm{~ H z}
$$
$$
Q_{0 1}
\approx2 \ 1 7 0
$$
I. $$
3. 8 9 \times1 0^{9} \mathrm{~ H z}
$$
$$
Q_{0 1}
\approx1 \ 9 6 0
$$
J. $$
4. 3 5 \times1 0^{9} \mathrm{~ H z}
$$
$$
Q_{0 1}
\approx2 \ 7 8 0
$$
Answer: E
A coaxial cavity with a length of $l=5$ cm and operating in the $\lambda_{0} / 2$ mode exhibits the TEM mode. The radii of its inner and outer conductors are $a=0.4 \; \text{cm}, \; b=1.2 \; \text{cm}$ respectively, with air filling the space between the conductors. The cavity material is brass. Calculate the quality factor $Q_{0}$ of this coaxial configuration.

Options:
A. 2333
B. 2175
C. 2340
D. 2150
E. 2230
F. 2256
G. 2290
H. 2249
I. 2385
J. 2268
Answer: H
The height of a vertical dipole antenna is $h = 10 \, \mathrm{m}$. When the operating wavelength is $\lambda = 300 \, \mathrm{m}$, determine its effective height and the radiation resistance attributed to the antinode current.

Options:
A. $$
R_{r} \approx0. 0 5 0 \ \Omega
$$
B. $$
R_{r} \approx0. 0 1 1 \ \Omega
$$
C. $$
R_{r} \approx0. 0 4 5 \ \Omega
$$
D. $$
R_{r} \approx0. 0 7 0 \ \Omega
$$
E. $$
R_{r} \approx0. 0 1 9 \ \Omega
$$
F. $$
R_{r} \approx0. 0 2 5 \ \Omega
$$
G. $$
R_{r} \approx0. 0 2 0 \ \Omega
$$
H. $$
R_{r} \approx0. 0 6 0 \ \Omega
$$
I. $$
R_{r} \approx0. 0 1 5 \ \Omega
$$
J. $$
R_{r} \approx0. 0 3 0 \ \Omega
$$
Answer: E
Try to design the E-plane and H-plane sectoral horn according to the optimal design scheme. It is known that the gain $G = 12 \, \mathrm{dB}$, the operating wavelength $\lambda = 3.2 \; \mathrm{cm}$, and the rectangular waveguide is chosen as the standard BJ-100 type waveguide. ② Find the values of $2 \theta_{0.5E}$ and $2 \theta_{0.5H}$.

Options:
A. $$
1 8. 3 4^{\circ},1 2. 2 0^{\circ}
$$
B. $$
2 0. 0 0^{\circ},1 1. 5 0^{\circ}
$$
C. $$
2 0. 3 1^{\circ},1 2. 5 7^{\circ}
$$
D. $$
1 9. 5 7^{\circ},1 0. 9 6^{\circ}
$$
E. $$
2 2. 0 4^{\circ},1 0. 0 5^{\circ}
$$
F. $$
2 1. 0 5^{\circ},1 0. 8 0^{\circ}
$$
G. $$
2 1. 6 1^{\circ},9 . 9 9^{\circ}
$$
H. $$
1 6. 8 8^{\circ},1 4. 0 0^{\circ}
$$
I. $$
1 7. 5 2^{\circ},1 3. 8 8^{\circ}
$$
J. $$
1 9. 9 9^{\circ},1 2. 0 7^{\circ}
$$
Answer: D
In unbounded space, the electric potential generated by the charge distribution $\rho$ in the spherical coordinate system is $\varphi = \frac{q}{4\pi\varepsilon_0} \left[ \left( \frac{1}{a} + \frac{1}{r} \right) e^{-\frac{2r}{a}} - \frac{1}{r} \right]$, where $q$ and $a$ are constants, and $r$ is the distance from the field point to the origin. Try to determine $\rho$.

Options:
A. $\rho = \frac{2q}{\pi a^3} e^{-\frac{2r}{a}}$
B. $\rho = \frac{q}{\pi a^3} e^{-\frac{r}{a}}$
C. $\rho = \frac{q}{\pi a^2} e^{-\frac{2r}{a}}$
D. $\rho = \frac{q}{2 \pi a^3} e^{-\frac{2r}{a}}$
E. $\rho = -\frac{q}{4 \pi a^3} e^{-\frac{2r}{a}}$
F. $\rho = -\frac{q}{2 \pi a^3} e^{-\frac{4r}{a}}$
G. $\rho = -\frac{q}{\pi a^3} e^{-\frac{r}{a}}$
H. $\rho = -\frac{q}{\pi a^2} e^{-\frac{2r}{a}}$
I. $\rho = \frac{q}{\pi a^3} e^{-\frac{4r}{a}}$
J. $\rho = -\frac{q}{\pi a^3} e^{-\frac{2r}{a}}$
Answer: J
Near the surface of the Sun, there is a blackbody sphere with a density of $\rho = 1.0 \times 10^{3} \mathrm{kg/m}^{3}$. Assume that the radiation pressure exerted on it by the Sun is equal to the gravitational attraction of the Sun on the sphere. Determine its radius. It is known that the radiation intensity from the Sun at the surface of the Earth's atmosphere is $1.35 \mathrm{kW/m}^{2}$, and the distance from the Earth to the Sun is $1.5 \times 10^{8} \mathrm{km}$.

Options:
A. $5.1 \times 10^{-7}(m)$
B. $6.4 \times 10^{-8}(m)$
C. $8.5 \times 10^{-4}(m)$
D. $1.9 \times 10^{-7}(m)$
E. $4.5 \times 10^{-9}(m)$
F. $7.2 \times 10^{-9}(m)$
G. $1.1 \times 10^{-6}(m)$
H. $3.2 \times 10^{-8}(m)$
I. $2.7 \times 10^{-6}(m)$
J. $9.8 \times 10^{-5}(m)$
Answer: D
A cave is exactly 1 km long, and when a train is stationary, it is also 1 km in length. When the train travels at a speed of 0.600c and passes through the cave, A is an observer standing on the ground, and B is an observer sitting on the train. How much time does A observe from the front end of the train entering the cave to the rear end exiting the cave?

Options:
A. $\Delta t = 8.00 \times 10^{-5}(s)$
B. $\Delta t = 5.00 \times 10^{-5}(s)$
C. $\Delta t = 9.00 \times 10^{-5}(s)$
D. $\Delta t = 1.10 \times 10^{-5}(s)$
E. $\Delta t = 3.00 \times 10^{-5}(s)$
F. $\Delta t = 4.00 \times 10^{-5}(s)$
G. $\Delta t = 7.00 \times 10^{-5}(s)$
H. $\Delta t = 6.00 \times 10^{-5}(s)$
I. $\Delta t = 2.00 \times 10^{-5}(s)$
J. $\Delta t = 1.00 \times 10^{-5}(s)$
Answer: J
A person bought a total of 11 fruits, of which 3 are second-grade and 8 are first-grade. The fruits are randomly distributed among $A$, $B$, and $C$, with each person receiving 4, 6, and 1 fruit, respectively. What is the probability that both $A$ and $B$ receive second-grade fruits while $C$ does not receive any second-grade fruit?

Options:
A. $$
{\frac{3 1} {5 5}}
$$
B. $$
{\frac{2 1} {5 5}}
$$
C. $$
{\frac{3 2} {6 5}}
$$
D. $$
{\frac{3 2} {5 4}}
$$
E. $$
{\frac{3 2} {4 5}}
$$
F. $$
{\frac{2 2} {5 5}}
$$
G. $$
{\frac{3 2} {5 5}}
$$
H. $$
{\frac{3 3} {5 5}}
$$
I. $$
{\frac{4 2} {5 5}}
$$
J. $$
{\frac{3 2} {5 6}}
$$
Answer: G
Given \( $P(A) = \frac{1}{2}, P(B) = \frac{1}{3}, P(C) = \frac{1}{5}, P(AB) = \frac{1}{10}, P(AC) = \frac{1}{15}, P(BC) = \frac{1}{20},$ $P(ABC) = \frac{1}{30}$ \). What are the probabilities of \( $A \cup B, \overline{AB}, A \cup B \cup C, \overline{ABC}, \overline{AB} \subseteq \overline{AB} \cup C$ \)?

Options:
A. $$
\frac{2} {1 5}+\frac{1} {3}-\frac{3} {2 0}=\frac{7} {3 0}
$$
B. $$
\frac{1} {2}+\frac{1} {3}-\frac{1} {1 5}=\frac{29} {3 0}
$$
C. $$
\frac{5} {1 0}+\frac{1} {3}-\frac{2} {1 5}=\frac{1} {9}
$$
D. $$
\frac{2} {1 0}+\frac{1} {5}-\frac{2} {3 0}=\frac{1} {1 0}
$$
E. $$
\frac{3} {5}+\frac{1} {3}-\frac{1} {2 0}=\frac{8} {1 5}
$$
F. $$
\frac{3} {4}+\frac{1} {5}-\frac{3} {2 0}=\frac{3} {1 0}
$$
G. $$
\frac{1} {2}+\frac{1} {4}-\frac{1} {1 0}=\frac{3} {1 5}
$$
H. $$
\frac{1} {6}+\frac{1} {4}-\frac{1} {1 5}=\frac{9} {2 0}
$$
I. $$
\frac{2} {5}+\frac{1} {3}-\frac{5} {3 0}=\frac{2} {1 0}
$$
J. $$
\frac{4} {1 5}+\frac{1} {5}-\frac{7} {6 0}=\frac{7} {2 0}
$$
Answer: J
A student takes the same course exam twice consecutively. The probability of passing the first time is $p$. If they pass the first time, the probability of passing the second time is also $p$; if they do not pass the first time, the probability of passing the second time is $\frac{p}{2}$. Given that he has passed the second time, what is the probability that he passed the first time?

Options:
A. $$
\frac{2p^{2}} {p^{2}+\frac{p} {2} ( 2-p )}-\frac{4p} {p+1}.
$$
B. $$
\frac{p} {p^{2}+\frac{p} {2} ( 1-2p )}-\frac{2p^{2}} {p+1}.
$$
C. $$
\frac{2p} {p^{2} + \frac{p} {4}(1-2p)}-\frac{p^{2}} {p + 3}.
$$
D. $$
\frac{p^{3}} {p^{2} - \frac{p} {2} ( 1+p )}-\frac{3p} {p+1}.
$$
E. $$
\frac{p^{2}} {p^{2}+\frac{p} {2} ( 1-p )}-\frac{2 p} {p+1}.
$$
F. $$
\frac{p^{2}} {3p^{2}+\frac{p} {2} ( 1-p )}-\frac{p} {p+3}.
$$
G. $$
\frac{2p^{2}} {p^{2}+\frac{3p} {2} (1-p)}-\frac{p} {2p+1}.
$$
H. $$
\frac{3p^{2}} {2p^{2}+p( 1-2p )}-\frac{1} {p+2}.
$$
I. $$
\frac{3p^{2}} {p^{2}+\frac{2p} {3} ( 1-p )}-\frac{p} {p+2}.
$$
J. $$
\frac{p} {2}-\frac{p^{2}} {p(1-p) + \frac{p} {3}}.
$$
Answer: E
A public opinion poll indicates that, among a simple random sample of 840 men and 750 women, 16% and 25%, respectively, support legislation to ban the sale of spirits nationwide. $( Z_{0.025}=1.96 \,, \, \, Z_{0.05}=1.645 )$ Please write the 95% confidence interval for the difference in the proportion of men and women who support this legislation is().

Options:
A. 6.35%- 11.82%.
B. 4.88%- 12.14%.
C. 5.75%- 13.21%.
D. 5.03%- 12.97%.
E. 2.94%- 9.42%.
F. 6.12%- 13.55%.
G. 4.22%- 11.37%.
H. 8.07%- 14.98%.
I. 3.47%- 10.56%.
J. 7.89%- 15.34%.
Answer: D
Using a stirrer, 41.84 J of work is done on 1 mol of a diatomic ideal gas, increasing its temperature by 1 K at constant pressure. If the gas's \( $C_{p, \, \mathrm{m}} = 29.28 \, \mathrm{J} \cdot \mathrm{mol}^{-1} \cdot \mathrm{K}^{-1}$ \), determine the process's \( $Q$ \), \( $W$ \), and the system's $\Delta U$ and $\Delta H$ is_____.

Options:
A. $$
2 0. \ 0 3 \ \mathrm{J}
$$
$$
3 2. 8 4 \mathrm{~ J}
$$
$$
2 7. 2 1 \mathrm{~ J}
$$
$$
6 9. 9 9 {\mathrm{~ J}}
$$
B. $$
2 6. \ 9 9 \ \mathrm{J}
$$
$$
3 8. 5 7 \mathrm{~ J}
$$
$$
2 2. 8 0 \mathrm{~ J}
$$
$$
7 5. 4 0 {\mathrm{~ J}}
$$
C. $$
2 7. \ 9 3 \ \mathrm{J}
$$
$$
3 5. 6 1 \mathrm{~ J}
$$
$$
2 5. 0 7 \mathrm{~ J}
$$
$$
7 2. 8 8 {\mathrm{~ J}}
$$
D. $$
2 3. \ 8 4 \ \mathrm{J}
$$
$$
3 1. 9 7 \mathrm{~ J}
$$
$$
1 9. 3 5 \mathrm{~ J}
$$
$$
7 1. 6 2 {\mathrm{~ J}}
$$
E. $$
2 4. \ 4 7 \ \mathrm{J}
$$
$$
3 4. 0 2 \mathrm{~ J}
$$
$$
2 3. 5 6 \mathrm{~ J}
$$
$$
7 4. 5 1 {\mathrm{~ J}}
$$
F. $$
2 5. \ 6 6 \ \mathrm{J}
$$
$$
3 2. 3 3 \mathrm{~ J}
$$
$$
1 9. 9 1 \mathrm{~ J}
$$
$$
7 6. 0 4 {\mathrm{~ J}}
$$
G. $$
2 8. \ 1 8 \ \mathrm{J}
$$
$$
3 6. 2 5 \mathrm{~ J}
$$
$$
1 8. 6 8 \mathrm{~ J}
$$
$$
7 0. 5 6 {\mathrm{~ J}}
$$
H. $$
2 9. \ 4 5 \ \mathrm{J}
$$
$$
3 0. 7 6 \mathrm{~ J}
$$
$$
2 6. 4 4 \mathrm{~ J}
$$
$$
7 3. 8 3 {\mathrm{~ J}}
$$
I. $$
2 9. \ 1 0 \ \mathrm{J}
$$
$$
3 3. 5 3 \mathrm{~ J}
$$
$$
2 0. 7 9 \mathrm{~ J}
$$
$$
7 0. 9 4 {\mathrm{~ J}}
$$
J. $$
2 1. \ 5 0 \ \mathrm{J}
$$
$$
3 0. 4 2 \mathrm{~ J}
$$
$$
2 2. 1 9 \mathrm{~ J}
$$
$$
6 8. 3 7 {\mathrm{~ J}}
$$
Answer: I
At 333 K, the vapor pressures of aniline (A) and water (B) are 0.760 kPa and 19.9 kPa, respectively. At this temperature, aniline and water are partially miscible, forming two phases. The mole fractions of aniline in the two phases are 0.732 (in the aniline layer) and 0.088 (in the water layer). Calculate the Henry's constant for aniline and water. Assume that the solvent in each phase obeys Raoult's law, and the solute obeys Henry's law.

Options:
A. $$
6 7. 7 \mathrm{~ k P a}
$$
B. $$
7 3. 8 \mathrm{~ k P a}
$$
C. $$
8 0. 2 \mathrm{~ k P a}
$$
D. $$
2 8. 6 \mathrm{~ k P a}
$$
E. $$
1 4. 1 \mathrm{~ k P a}
$$
F. $$
3 4. 5 \mathrm{~ k P a}
$$
G. $$
9 6. 4 \mathrm{~ k P a}
$$
H. $$
5 2. 1 \mathrm{~ k P a}
$$
I. $$
5 9. 7 \mathrm{~ k P a}
$$
J. $$
4 5. 9 \mathrm{~ k P a}
$$
Answer: A
At room temperature, liquid A and liquid B can form an ideal liquid mixture. There is currently a vapor phase of this mixture, where the mole fraction of A is 0.4, and it is placed in a cylinder with a piston. The cylinder is slowly compressed at room temperature. It is known that the saturation vapor pressures of pure liquid A and liquid B are \( P_{A}^{\ast} = 40.0 \ \mathrm{kPa} \) and \( P_{B}^{\ast} = 120.0 \ \mathrm{kPa} \), respectively. Determine the total pressure of the gas inside the cylinder when the liquid starts to appear.

Options:
A. $$
9 0. 9 0 \mathrm{~ k P a}
$$
B. $$
9 9. 9 9 \mathrm{~ k P a}
$$
C. $$
8 8. 8 8 \mathrm{~ k P a}
$$
D. $$
7 5. 7 5 \mathrm{~ k P a}
$$
E. $$
6 0. 0 0 \mathrm{~ k P a}
$$
F. $$
1 2 0 \mathrm{~ k P a}
$$
G. $$
1 0 0 \mathrm{~ k P a}
$$
H. $$
6 6. 6 6 \mathrm{~ k P a}
$$
I. $$
7 7. 7 7 \mathrm{~ k P a}
$$
J. $$
5 5. 5 5 \mathrm{~ k P a}
$$
Answer: H
Given the reaction \( ($\mathrm{CH}_{3})_{2} \mathrm{CHOH} (\mathrm{g}$) = ($\mathrm{CH}_{3})_{2} \mathrm{CO} (\mathrm{g}) + \mathrm{H}_{2} (\mathrm{g}$) \), where \($\Delta C_{p, \mathrm{m}}^{\ominus}$ = $16.72 \text{ J} \cdot \text{mol}^{-1} \cdot \text{K}^{-1}$\). At \($457 \text{ K}$\), \($K_{p}^{\Theta}$ = $0.36$\), and at \($298 \text{ K}$\), \($\Delta_{\mathrm{r}} H_{\mathrm{m}}^{\ominus}$ = $61.5 \text{ kJ} \cdot \text{mol}^{-1}$\). Write the functional relationship of \($\ln K_{p}^{\Theta} - f(T)$\) .

Options:
A. $$
\operatorname{l n} \, K_{p}^{\Theta} \left( \, T \, \right) \,=0. \, 6 7 1 \,+1. \, 3 2 9 \, \times\operatorname{l n} \, \left( \, T / K \, \right) \,+\frac{3 \, 2 1 6. \, 5 8} {T / K}
$$
B. $$
\operatorname{l n} \, K_{p}^{\Theta} \left( \, T \, \right) \,=2. \, 5 3 3 \,+1. \, 5 0 1 \, \times\operatorname{l n} \, \left( \, T / K \, \right) \,-\frac{7 \, 8 9 6. \, 4 2} {T / K}
$$
C. $$
\operatorname{l n} \, K_{p}^{\Theta} \left( \, T \, \right) \,=1. \, 5 3 3 \,+2. \, 0 1 1 \, \times\operatorname{l n} \, \left( \, T / K \, \right) \,-\frac{6 \, 7 9 7. \, 8 6} {T / K}
$$
D. $$
\operatorname{l n} \, K_{p}^{\Theta} \left( \, T \, \right) \,=1. \, 7 5 4 \,-2. \, 3 4 5 \, \times\operatorname{l n} \, \left( \, T / K \, \right) \,+\frac{9 \, 0 1 2. \, 8 3} {T / K}
$$
E. $$
\operatorname{l n} \, K_{p}^{\Theta} \left( \, T \, \right) \,=1. \, 9 5 6 \,-0. \, 8 0 7 \, \times\operatorname{l n} \, \left( \, T / K \, \right) \,+\frac{7 \, 8 5 3. \, 3 2} {T / K}
$$
F. $$
\operatorname{l n} \, K_{p}^{\Theta} \left( \, T \, \right) \,=1. \, 2 0 8 \,+0. \, 4 5 6 \, \times\operatorname{l n} \, \left( \, T / K \, \right) \,-\frac{8 \, 3 9 0. \, 4 9} {T / K}
$$
G. $$
\operatorname{l n} \, K_{p}^{\Theta} \left( \, T \, \right) \,=3. \, 2 3 1 \,-1. \, 0 9 8 \, \times\operatorname{l n} \, \left( \, T / K \, \right) \,-\frac{3 \, 8 4 5. \, 1 7} {T / K}
$$
H. $$
\operatorname{l n} \, K_{p}^{\Theta} \left( \, T \, \right) \,=2. \, 0 4 9 \,+1. \, 7 6 8 \, \times\operatorname{l n} \, \left( \, T / K \, \right) \,-\frac{6 \, 2 1 5. \, 3 4} {T / K}
$$
I. $$
\operatorname{l n} \, K_{p}^{\Theta} \left( \, T \, \right) \,=0. \, 9 8 7 \,+3. \, 1 0 2 \, \times\operatorname{l n} \, \left( \, T / K \, \right) \,+\frac{5 \, 4 8 9. \, 5 2} {T / K}
$$
J. $$
\operatorname{l n} \, K_{p}^{\Theta} \left( \, T \, \right) \,=1. \, 0 2 7 \,+1. \, 1 9 7 \, \times\operatorname{l n} \, \left( \, T / K \, \right) \,-\frac{5 \, 4 3 8. \, 9 1} {T / K}
$$
Answer: C
At 298 K, the conductivity of a saturated aqueous solution of $\mathrm{SrSO}_{4}$ is measured to be $\kappa_{\mathrm{if\!f}} = 1.482 \times 10^{-2} \, \mathrm{S \cdot m^{-1}}$, and the conductivity of water at this temperature is $\kappa_{\mathrm{H_{2}O}} = 1.496 \times 10^{-4} \, \mathrm{S \cdot m^{-1}}$. Please calculate the concentration of the saturated solution of SrSO in water under these conditions.

Options:
A. $$
2. \, 5 6 4 \, \times\, 1 0^{-3} \, \, \mathrm{m o l} \, \cdot\, \mathrm{d m}^{-3}
$$
B. $$
6. \, 7 5 3 \, \times\, 1 0^{-6} \, \, \mathrm{m o l} \, \cdot\, \mathrm{d m}^{-3}
$$
C. $$
1. \, 0 4 9 \, \times\, 1 0^{-8} \, \, \mathrm{m o l} \, \cdot\, \mathrm{d m}^{-3}
$$
D. $$
9. \, 2 1 8 \, \times\, 1 0^{-5} \, \, \mathrm{m o l} \, \cdot\, \mathrm{d m}^{-3}
$$
E. $$
7. \, 4 5 0 \, \times\, 1 0^{-2} \, \, \mathrm{m o l} \, \cdot\, \mathrm{d m}^{-3}
$$
F. $$
3. \, 8 4 2 \, \times\, 1 0^{-3} \, \, \mathrm{m o l} \, \cdot\, \mathrm{d m}^{-3}
$$
G. $$
4. \, 1 9 0 \, \times\, 1 0^{-5} \, \, \mathrm{m o l} \, \cdot\, \mathrm{d m}^{-3}
$$
H. $$
2. \, 9 7 1 \, \times\, 1 0^{-7} \, \, \mathrm{m o l} \, \cdot\, \mathrm{d m}^{-3}
$$
I. $$
8. \, 3 5 7 \, \times\, 1 0^{-6} \, \, \mathrm{m o l} \, \cdot\, \mathrm{d m}^{-3}
$$
J. $$
5. \, 2 6 8 \, \times\, 1 0^{-4} \, \, \mathrm{m o l} \, \cdot\, \mathrm{d m}^{-3}
$$
Answer: J
In a sealed bell jar, there is a cup of pure water A and a cup of sugar water B. After standing for a sufficiently long time, it is found that_____.

Options:
A. Cup A evaporated entirely, Cup B stayed unchanged.
B. Cup A absorbed outside air, Cup B bubbled intensely.
C. Cup A became cloudy, Cup B remained clear throughout.
D. Cup A shrank slightly, Cup B swelled just a little.
E. Cup A emitted vapor, Cup B lost minimal liquid.
F. Cup A turned into ice, Cup B became icy but didn't overflow.
G. Cup A grew a salt layer, Cup B stayed unchanged.
H. Cup A is full, and Cup B remains half-empty.
I. Cup A reduced to an empty cup, Cup B overflowed when full.
J. Cup A gained weight, Cup B had no visible change.
Answer: I
Molecular weight of solids. For $\mathbf{H}_{2}$, the Lennard-Jones parameters obtained from gas measurements are $\varepsilon\ =50 \times10^{-16} \ \mathrm{erg}, \ \ \sigma=2.96 \ \mathrm{Å}$ . Calculate the binding energy of $\mathbf{H}_{2}$ in fcc structure (in KJ/mol), treating each hydrogen molecule as spherical. The experimental value of the binding energy is 0.751 KJ/mol. Please compare the experimental value of the binding energy with the calculated value.

Options:
A. $$
U_{t o t}
\approx-1. 4 8 \mathrm{K J / m o l}
$$
B. $$
U_{t o t}
\approx-0. 9 5 \mathrm{K J / m o l}
$$
C. $$
U_{t o t}
\approx-0. 6 3 \mathrm{K J / m o l}
$$
D. $$
U_{t o t}
\approx-3. 9 1 \mathrm{K J / m o l}
$$
E. $$
U_{t o t}
\approx-1. 1 0 \mathrm{K J / m o l}
$$
F. $$
U_{t o t}
\approx-4. 0 2 \mathrm{K J / m o l}
$$
G. $$
U_{t o t}
\approx-3. 2 5 \mathrm{K J / m o l}
$$
H. $$
U_{t o t}
\approx-1. 7 6 \mathrm{K J / m o l}
$$
I. $$
U_{t o t}
\approx-2. 8 7 \mathrm{K J / m o l}
$$
J. $$
U_{t o t}
\approx-2. 5 5 \mathrm{K J / m o l}
$$
Answer: J
Given the mass of the Sun as $M_{\odot} = 2 \times 10^{33} \text{g}$, try to estimate the number of electrons in the Sun. If the same number of electrons can be ionized in a white dwarf and confined within a sphere of radius $2 \times 10^{9} \text{m}$, the Fermi energy of the electrons is (), expressed in electron volts (eV).

Options:
A. $$
\approx5. 2 \times1 0^{3} \mathrm{e V}
$$
B. $$
\approx1. 3 \times1 0^{3} \mathrm{e V}
$$
C. $$
\approx8. 3 \times1 0^{3} \mathrm{e V}
$$
D. $$
\approx9. 9 \times1 0^{2} \mathrm{e V}
$$
E. $$
\approx6. 4 \times1 0^{2} \mathrm{e V}
$$
F. $$
\approx3. 9 \times1 0^{4} \mathrm{e V}
$$
G. $$
\approx4. 7 \times1 0^{5} \mathrm{e V}
$$
H. $$
\approx2. 5 \times1 0^{4} \mathrm{e V}
$$
I. $$
\approx7. 8 \times1 0^{5} \mathrm{e V}
$$
J. $$
\approx2. 1 \times1 0^{5} \mathrm{e V}
$$
Answer: H
In a specific semiconductor containing $1 \times 10^{13} \ \mathrm{cm}^{-3}$ donors, with an ionization energy of 1 mev and an effective mass of 0.01 m, the concentration of conduction electrons at 4 K is estimatedly ().

Options:
A. $$
3. 8 9 0 \times1 0^{1 3} \mathrm{c m}^{-3}
$$
B. $$
0. 5 7 2 \times1 0^{1 3} \mathrm{c m}^{-3}
$$
C. $$
0. 6 8 9 \times1 0^{1 3} \mathrm{c m}^{-3}
$$
D. $$
1. 2 9 4 \times1 0^{1 3} \mathrm{c m}^{-3}
$$
E. $$
2. 5 1 3 \times1 0^{1 3} \mathrm{c m}^{-3}
$$
F. $$
0. 3 5 4 \times1 0^{1 3} \mathrm{c m}^{-3}
$$
G. $$
4. 1 7 6 \times1 0^{1 3} \mathrm{c m}^{-3}
$$
H. $$
0. 7 2 1 \times1 0^{1 3} \mathrm{c m}^{-3}
$$
I. $$
1. 0 0 5 \times1 0^{1 3} \mathrm{c m}^{-3}
$$
J. $$
0. 1 0 8 \times1 0^{1 3} \mathrm{c m}^{-3}
$$
Answer: J
Based on the free electron model, calculate the period $\Delta(1 / B)$ for potassium, which is ().

Options:
A. $$
5. 2 8 \times1 0^{-6} \mathbf{G a u s s}^{-1}
$$
B. $$
7. 1 3 \times1 0^{-9} \mathbf{G a u s s}^{-1}
$$
C. $$
6. 3 8 \times1 0^{-8} \mathbf{G a u s s}^{-1}
$$
D. $$
2. 7 9 \times1 0^{-8} \mathbf{G a u s s}^{-1}
$$
E. $$
3. 5 4 \times1 0^{-9} \mathbf{G a u s s}^{-1}
$$
F. $$
5. 9 7 \times1 0^{-8} \mathbf{G a u s s}^{-1}
$$
G. $$
8. 6 4 \times1 0^{-7} \mathbf{G a u s s}^{-1}
$$
H. $$
4. 9 5 \times1 0^{-7} \mathbf{G a u s s}^{-1}
$$
I. $$
5. 4 6 \times1 0^{-8} \mathbf{G a u s s}^{-1}
$$
J. $$
9. 8 5 \times1 0^{-8} \mathbf{G a u s s}^{-1}
$$
Answer: I
The $\mathsf{C u}_{3} \mathsf{A u}$ alloy (75% Cu, 25% Au) exhibits an ordered state below 400°C, wherein Au atoms occupy the position 000 of the face centered cubic, while Cu atoms accupy the positions $\frac{1}{2} \frac{1}{2} 0, \frac{1}{2} 0 \frac{1}{2}$, and $0 \frac{1}{2} \frac{1}{2}$. Provide the indices of the x-ray reflections that newly appear when the alloy transitions from a disordered to an ordered state. List all the new reflections with indices ≤ 2, which include _____.

Options:
A. (212), (121), (211), (102), (201), (120); (122), (101), (012), (220), (112), (011).
B. (111), (112), (121), (211), (120), (102); (101), (201), (211), (010), (110), (012).
C. (010), (100), (001), (012), (102), (201); (111), (211), (012), (110), (021), (121).
D. (002), (020), (200), (211), (121), (212); (101), (110), (120), (201), (210), (122).
E. (101), (110), (111), (113), (114), (115); (011), (112), (211), (102), (202), (212).
F. (110), (101), (011), (210), (120), (201); (202), (212), (222), (012), (102), (221).
G. (011), (101), (110), (112), (120), (210); (012), (201), (211), (022), (122), (221).
H. (021), (120), (102), (210), (101), (011); (221), (112), (110), (201), (121), (211).
I. (220), (202), (211), (121), (210), (120); (201), (110), (101), (112), (011), (222).
J. (012), (021), (102), (201), (120), (210); (011), (101), (110), (211), (121), (112).
Answer: J
Find the frequency distribution function $g(\omega)$ of a one-dimensional monoatomic chain.

Options:
A. $$
g ( \omega)=\frac{\mathrm{d} n} {\mathrm{d} \omega}=\frac{N a} {\pi} \frac{2} {a \omega_{\mathrm{m}} \left| \operatorname{s i n} \frac{1} {4} a q \right|}=\frac{2 N} {\pi\sqrt{\omega^{2}-\omega_{\mathrm{m}}^{4}}}
$$
B. $$
g ( \omega)=\frac{\mathrm{d} n} {\mathrm{d} \omega}=\frac{N a} {\pi} \frac{2} {a \omega_{\mathrm{m}} \left| \operatorname{c o s} \frac{1} {2} a q \right|}=\frac{2 N} {\pi\sqrt{\omega_{\mathrm{m}}^{2}-\omega^{2}}}
$$
C. $$
g ( \omega)=\frac{\mathrm{d} n} {\mathrm{d} \omega}=\frac{N a} {\pi} \frac{2} {a \omega_{\mathrm{m}} \left| \operatorname{c o s} a q \right|}=\frac{2 N} {\pi\sqrt{\omega_{\mathrm{m}}^{2}-2\omega^{2}}}
$$
D. $$
g ( \omega)=\frac{\mathrm{d} n} {\mathrm{d} \omega}=\frac{\pi} {N a} \frac{2} {a \omega_{\mathrm{m}} \left| \operatorname{c o s} a q \right|}=\frac{2 N} {\pi\sqrt{\omega^{3}-\omega_{\mathrm{m}}^{2}}}
$$
E. $$
g ( \omega)=\frac{\mathrm{d} n} {\mathrm{d} \omega}=\frac{N a} {\pi} \frac{2} {\omega_{\mathrm{m}} a \left| \operatorname{s i n} \frac{1} {2} a q \right|}=\frac{2 N} {\sqrt{\omega_{\mathrm{m}}^{2}+\omega^{2}}}
$$
F. $$
g ( \omega)=\frac{\mathrm{d} n} {\mathrm{d} \omega}=\frac{N} {a} \frac{2} {\pi \omega_{\mathrm{m}} \left| \operatorname{s i n} \frac{1} {2} a q \right|}=\frac{2 \pi} {N\sqrt{\omega_{\mathrm{m}}^{2}+\omega^{2}}}
$$
G. $$
g ( \omega)=\frac{\mathrm{d} n} {\mathrm{d} \omega}=\frac{N} {a} \frac{2} {\pi \omega_{\mathrm{m}} \left| \operatorname{c o s} \frac{3} {2} a q \right|}=\frac{2 N} {\pi\sqrt{\omega_{\mathrm{m}}^{2}-\omega^{2}}}
$$
H. $$
g ( \omega)=\frac{\mathrm{d} n} {\mathrm{d} \omega}=\frac{N a} {\pi} \frac{2} {a \omega_{\mathrm{m}} \left| \operatorname{s i n} 2 a q \right|}=\frac{2 \omega^{2}} {\pi\sqrt{N^{2}-\omega_{\mathrm{m}}^{2}}}
$$
I. $$
g ( \omega)=\frac{\mathrm{d} n} {\mathrm{d} \omega}=\frac{N} {a} \frac{2} {\pi \omega_{\mathrm{m}} \left| \operatorname{s i n} \frac{1} {2} a q \right|}=\frac{2 N} {\pi\sqrt{\omega^{2}-\omega_{\mathrm{m}}^{2}}}
$$
J. $$
g ( \omega)=\frac{\mathrm{d} n} {\mathrm{d} \omega}=\frac{N} {a} \frac{2} {a \omega_{\mathrm{m}} \left| \operatorname{c o s} \frac{1} {4} a q \right|}=\frac{2 N} {\pi\sqrt{\omega_{\mathrm{m}}^{4}+\omega^{3}}}
$$
Answer: B
Adding zinc to copper causes some copper atoms to be replaced by zinc atoms. Using the free electron model, determine the ratio of zinc atoms to copper atoms at which the Fermi sphere contacts the first Brillouin zone boundary. (Copper has a face-centered cubic lattice and is monovalent, while zinc is divalent.)
$${\frac{n_{Zn}} {n_{Cu}}=}$$

Options:
A. $$
{\frac{7} {1 3}}
$$
B. $$
{\frac{5} {1 2}}
$$
C. $$
{\frac{8} {1 5}}
$$
D. $$
{\frac{9} {1 6}}
$$
E. $$
{\frac{1 1} {1 8}}
$$
F. $$
{\frac{1 3} {2 0}}
$$
G. $$
{\frac{1 1} {1 5}}
$$
H. $$
{\frac{1 4} {1 7}}
$$
I. $$
{\frac{6} {1 9}}
$$
J. $$
{\frac{5} {1 4}}
$$
Answer: D
For $\mathbf{B}=10K \mathbf{G}=1T$, what is the area of the extremal orbit in real space?

Options:
A. $$
6. 4 4 7 \times1 0^{-5} \mathrm{c m}^{2}
$$
B. $$
7. 9 9 0 \times1 0^{-5} \mathrm{c m}^{2}
$$
C. $$
3. 5 5 6 \times1 0^{-5} \mathrm{c m}^{2}
$$
D. $$
0. 7 5 7 \times1 0^{-5} \mathrm{c m}^{2}
$$
E. $$
4. 7 0 3 \times1 0^{-5} \mathrm{c m}^{2}
$$
F. $$
8. 3 1 9 \times1 0^{-5} \mathrm{c m}^{2}
$$
G. $$
2. 9 1 2 \times1 0^{-5} \mathrm{c m}^{2}
$$
H. $$
1. 1 6 8 \times1 0^{-5} \mathrm{c m}^{2}
$$
I. $$
9. 2 1 5 \times1 0^{-5} \mathrm{c m}^{2}
$$
J. $$
5. 0 6 4 \times1 0^{-5} \mathrm{c m}^{2}
$$
Answer: D
In a certain cylinder, the gas expands from 0.1 $\mathrm{m}^{3}$ to 0.3 $\mathrm{m}^{3}$. If the pressure and volume of the gas are calculated in units of MPa and $\mathrm{m}^{3}$ respectively, then the functional relationship between the pressure and volume during the expansion process is given by $p=0.24V+0.04$. Find the work done by the gas during the expansion

Options:
A. $$
2. 0 \times1 0^{5} J
$$
B. $$
3. 2 \times1 0^{5} J
$$
C. $$
2. 5 \times1 0^{5} J
$$
D. $$
4. 1 \times1 0^{5} J
$$
E. $$
5. 9 \times1 0^{5} J
$$
F. $$
3. 0 \times1 0^{6} J
$$
G. $$
1. 0 \times1 0^{6} J
$$
H. $$
1. 8 \times1 0^{5} J
$$
I. $$
5. 0 \times1 0^{6} J
$$
J. $$
4. 5 \times1 0^{5} J
$$
Answer: H
For a certain stable flow system, it is known that the gas parameters at the inlet are $p_{1}=0.62 \mathrm{~MPa}$, $v_{2}=1.2 \mathrm{~m}^{3} / \mathrm{kg}$, $u_{1}=2100 \mathrm{~kJ/kg}$, and $c_{\textsf{fi}}=300 \mathrm{~m/s}$; at the outlet, the parameters are $v_{1}=0.37 \mathrm{~m}^{3} / \mathrm{kg}$, $p_{2}=0.13 \mathrm{~MPa}$, $500 \mathrm{~kJ/kg}$, and $c_{12}=150 \mathrm{~m/s}$. The mass flow rate of the gas is $q_{m}=4 \mathrm{~kg/s}$, and the heat transferred out of the system as the gas flows through is $30 \mathrm{kJ} / \mathrm{kg}$. Assuming changes in gravitational potential energy are negligible as the gas flows through the system, find the power output to the surroundings

Options:
A. $$
2 5 0 7. 8 k W
$$
B. $$
2 3 9 2. 7 k W
$$
C. $$
2 6 9 7. 3 k W
$$
D. $$
2 7 0 8. 6 k W
$$
E. $$
2 7 6 1. 4 k W
$$
F. $$
2 5 9 9. 2 k W
$$
G. $$
3 0 1 2. 1 k W
$$
H. $$
2 7 5 3. 9 k W
$$
I. $$
2 6 8 8. 5 k W
$$
J. $$
2 8 0 5. 4 k W
$$
Answer: D
An adiabatic rigid-body cylinder is divided into two parts by a thermally conductive, frictionless piston. Initially, the piston is fixed at a certain position, with one side of the cylinder containing 0.5 kg of an ideal gas at $0.4 MPa$ and $30°C$, while the other side contains the same gas at $1.2 MPa$, $30°C$, and $0.5 kg$. The piston is then released, allowing it to move freely until equilibrium is reached on both sides. Assuming constant specific heat capacity, determine the pressure (MPa) at equilibrium

Options:
A. $$
1. 8 7 \times1 0^{5} P a
$$
B. $$
2. 7 8 \times1 0^{9} P a
$$
C. $$
9. 5 6 \times1 0^{3} P a
$$
D. $$
8. 1 0 \times1 0^{2} P a
$$
E. $$
6. 2 1 \times1 0^{4} P a
$$
F. $$
1. 5 3 \times1 0^{8} P a
$$
G. $$
2. 4 5 \times1 0^{6} P a
$$
H. $$
4. 9 0 \times1 0^{5} P a
$$
I. $$
3. 0 2 \times1 0^{7} P a
$$
J. $$
5. 3 3 \times1 0^{6} P a
$$
Answer: A
Given that the boiler emits 10 m³ of flue gas for each 1 kg of coal burned (under standard conditions), and the coal consumption rate of the boiler is 30 t/h, the gas analyzer measures the volume fractions of the components in the flue gas as $φ_CO₂ = 0.12, φ_O₂ = 0.05, φ_N₂ = 0.79, φ_H₂O = 0.04$. The temperature of the flue gas in the chimney is $280^{\circ} \ \mathrm{C}$, and the pressure is 0.98 × 10⁵ Pa. Determine the volumetric flow rate of the flue gas in the chimney

Options:
A. $$
6. 2 8 \times1 0^{5} m^{3} / h
$$
B. $$
6. 1 9 \times1 0^{5} m^{3} / h
$$
C. $$
6. 5 5 \times1 0^{5} m^{3} / h
$$
D. $$
7. 0 2 \times1 0^{5} m^{3} / h
$$
E. $$
5. 8 4 \times1 0^{5} m^{3} / h
$$
F. $$
7. 1 0 \times1 0^{5} m^{3} / h
$$
G. $$
7. 4 7 \times1 0^{5} m^{3} / h
$$
H. $$
6. 3 5 \times1 0^{5} m^{3} / h
$$
I. $$
5. 9 3 \times1 0^{5} m^{3} / h
$$
J. $$
5. 7 6 \times1 0^{5} m^{3} / h
$$
Answer: A
Air undergoes reversible adiabatic flow in a converging nozzle. At section a, the parameters are \( $p_{a}$ = $0.5 \ \text{MPa}, \ t_{a}$ = $400 \ \degree\text{C}, \ c_{\text{f, s}}$ = $148 \ \text{m/s}$ \). The exit cross-sectional area of the nozzle is \( $25 \ \text{mm}^2$ \). Determine the maximum mass flow rate of the nozzle, the exit velocity, and the back pressure

Options:
A. $$
2. 4 k g / s
$$
$$
0. 5 8 9 m^{3} / k g
$$
$$481.60m/s$$
B. $$
2. 2 k g / s
$$
$$
0. 5 9 8 m^{3} / k g
$$
$$479.50m/s$$
C. $$
2. 0 k g / s
$$
$$
0. 6 0 4 m^{3} / k g
$$
$$475.30m/s$$
D. $$
2. 0 k g / s
$$
$$
0. 5 9 4 m^{3} / k g
$$
$$489.70m/s$$
E. $$
2. 1 k g / s
$$
$$
0. 5 8 2 m^{3} / k g
$$
$$488.88m/s$$
F. $$
1. 7 k g / s
$$
$$
0. 6 1 1 m^{3} / k g
$$
$$493.25m/s$$
G. $$
2. 5 k g / s
$$
$$
0. 5 8 0 m^{3} / k g
$$
$$482.90m/s$$
H. $$
1. 9 k g / s
$$
$$
0. 5 9 1 m^{3} / k g
$$
$$490.12m/s$$
I. $$
2. 3 k g / s
$$
$$
0. 5 7 2 m^{3} / k g
$$
$$485.75m/s$$
J. $$
1. 8 k g / s
$$
$$
0. 5 8 5 m^{3} / k g
$$
$$492.00m/s$$
Answer: E
Water vapor at $p_{1}=2 \ \mathrm{MPa}, \ \ t_{1}=300^{\circ} \ \mathrm{C}$ flows through a Laval nozzle into a space with a pressure of 0.1 MPa. Given that the minimum cross-sectional area of the nozzle is $A_{\operatorname* {min}}=2 \ \ \mathrm{cm}^{2}$, determine the critical velocity, exit velocity, mass flow rate per second, and the exit cross-sectional area under ideal conditions

Options:
A. $$
5 5 0. 5 \ \mathrm{m / s}
$$
$$
1 \ 1 5 0 \ \mathrm{m / s}
$$
$$
0. 5 5 5 \mathrm{\ k g / s}
$$
$$
8. 2 0 {\mathrm{~ c m}}^{2}
$$
B. $$
5 4 8. 5 \ \mathrm{m / s}
$$
$$
1 \ 1 0 0 \ \mathrm{m / s}
$$
$$
0. 5 4 8 \mathrm{\ k g / s}
$$
$$
7. 8 5 {\mathrm{~ c m}}^{2}
$$
C. $$
5 4 5. 0 \ \mathrm{m / s}
$$
$$
1 \ 1 2 0 \ \mathrm{m / s}
$$
$$
0. 5 4 5 \mathrm{\ k g / s}
$$
$$
7. 9 0 {\mathrm{~ c m}}^{2}
$$
D. $$
5 6 0. 0 \ \mathrm{m / s}
$$
$$
1 \ 2 0 0 \ \mathrm{m / s}
$$
$$
0. 5 6 0 \mathrm{\ k g / s}
$$
$$
8. 0 0 {\mathrm{~ c m}}^{2}
$$
E. $$
5 3 8. 5 \ \mathrm{m / s}
$$
$$
1 \ 0 7 1 \ \mathrm{m / s}
$$
$$
0. 5 3 9 \mathrm{\ k g / s}
$$
$$
7. 6 5 {\mathrm{~ c m}}^{2}
$$
F. $$
5 4 0. 0 \ \mathrm{m / s}
$$
$$
1 \ 1 0 0 \ \mathrm{m / s}
$$
$$
0. 5 4 0 \mathrm{\ k g / s}
$$
$$
7. 8 0 {\mathrm{~ c m}}^{2}
$$
G. $$
5 3 9. 5 \ \mathrm{m / s}
$$
$$
1 \ 0 9 5 \ \mathrm{m / s}
$$
$$
0. 5 3 9 \mathrm{\ k g / s}
$$
$$
7. 6 8 {\mathrm{~ c m}}^{2}
$$
H. $$
5 6 2. 0 \ \mathrm{m / s}
$$
$$
1 \ 2 1 0 \ \mathrm{m / s}
$$
$$
0. 5 6 2 \mathrm{\ k g / s}
$$
$$
8. 1 5 {\mathrm{~ c m}}^{2}
$$
I. $$
5 3 5. 0 \ \mathrm{m / s}
$$
$$
1 \ 0 9 0 \ \mathrm{m / s}
$$
$$
0. 5 3 0 \mathrm{\ k g / s}
$$
$$
7. 7 0 {\mathrm{~ c m}}^{2}
$$
J. $$
5 3 3. 5 \ \mathrm{m / s}
$$
$$
1 \ 0 8 0 \ \mathrm{m / s}
$$
$$
0. 5 3 3 \mathrm{\ k g / s}
$$
$$
7. 6 0 {\mathrm{~ c m}}^{2}
$$
Answer: E
For a certain maritime ideal steam power unit, the parameters of the fresh steam entering the turbine are $p_{1}=6 ~ \mathrm{MPa}, ~ ~ t_{1}=560^{\circ}\mathrm{C}$, and the steam pressure in the condenser is $6 \mathrm{kPa}$. Neglecting pump work, calculate the cycle thermal efficiency. If the power output of the unit is 10 $\mathrm{MW}$, determine the steam consumption per hour

Options:
A. $$
2 3. 7 5 t / h.
$$
B. $$
2 8. 9 5 t / h.
$$
C. $$
2 6. 0 0 t / h.
$$
D. $$
2 7. 1 3 t / h.
$$
E. $$
2 9. 0 4 t / h.
$$
F. $$
3 2. 4 8 t / h.
$$
G. $$
3 0. 5 0 t / h.
$$
H. $$
2 5. 9 1 t / h.
$$
I. $$
2 4. 8 5 t / h.
$$
J. $$
3 1. 2 1 t / h.
$$
Answer: H
In a certain ammonia vapor compression refrigeration cycle, the evaporation temperature is known to be $10^{\circ} \ \mathrm{C}$ and the condensation temperature is $30^{\circ} \ \mathrm{C}$. The compressor intake is dry saturated vapor, and the refrigeration capacity is $2 \times 10^{8} \ \mathrm{kJ/h}$. Determine the mass flow rate of the refrigerant for this refrigeration cycle and the theoretical power required by the compressor

Options:
A. $$
1 9 7 k g / h
$$
$$
5. 0 k W
$$
B. $$
1 7 5 k g / h
$$
$$
5. 9 k W
$$
C. $$
1 6 4 k g / h
$$
$$
4. 8 k W
$$
D. $$
1 5 6 k g / h
$$
$$
7. 5 k W
$$
E. $$
2 1 1 k g / h
$$
$$
8. 3 k W
$$
F. $$
1 4 3 k g / h
$$
$$
6. 1 k W
$$
G. $$
1 6 9 k g / h
$$
$$
5. 6 k W
$$
H. $$
2 2 0 k g / h
$$
$$
6. 7 k W
$$
I. $$
2 0 5 k g / h
$$
$$
7. 2 k W
$$
J. $$
1 8 2 k g / h
$$
$$
4. 9 k W
$$
Answer: G
Both water and air flow parallel over a flat plate at a speed of \( u_{\infty} = 1 \ \mathrm{m/s} \) with an average boundary layer temperature of \( 50^{\circ} \ \mathrm{C} \). Determine the thickness of the velocity boundary layer and the thermal boundary layer at a distance of \( 100 \ \mathrm{mm} \) from the leading edge of the plate

Options:
A. $$
6. 2 9 0 m m
$$
B. $$
4. 6 6 2 m m
$$
C. $$
9. 7 6 5 m m
$$
D. $$
5. 0 8 8 m m
$$
E. $$
1. 2 5 7 m m
$$
F. $$
6. 9 9 9 m m
$$
G. $$
2. 9 3 4 m m
$$
H. $$
3. 4 7 1 m m
$$
I. $$
8. 1 4 3 m m
$$
J. $$
7. 5 5 2 m m
$$
Answer: J
Water is fed into the boiler at a state of $p_{1}=10 \, \mathrm{MPa}$ and $t_{1}=220 \, \mathrm{C}$, and is heated at constant pressure until reaching $t_{2}=550 \, \mathrm{C}$, producing steam that exits the boiler. Calculate the amount of heat absorbed by each kilogram of water in the boiler

Options:
A. $$
2 5 2 9. 8 3 \mathrm{~ k J / k g}
$$
B. $$
2 6 1 0. 4 8 \mathrm{~ k J / k g}
$$
C. $$
2 5 5 3. 3 9 \mathrm{~ k J / k g}
$$
D. $$
2 6 0 5. 7 4 \mathrm{~ k J / k g}
$$
E. $$
2 4 9 3. 6 0 \mathrm{~ k J / k g}
$$
F. $$
2 5 7 8. 9 0 \mathrm{~ k J / k g}
$$
G. $$
2 4 7 0. 5 5 \mathrm{~ k J / k g}
$$
H. $$
2 5 4 4. 2 1 \mathrm{~ k J / k g}
$$
I. $$
2 5 0 1. 4 2 \mathrm{~ k J / k g}
$$
J. $$
2 5 8 1. 3 7 \mathrm{~ k J / k g}
$$
Answer: C
The roof of the building is covered with a layer of galvanized iron, which has an absorption coefficient of 0.5 for solar radiation and an emissivity of 0.2 If the incident solar radiation at noon in summer is $1000 \ \mathrm{W / m^{2}}$, the outdoor air temperature is 35°C, and the convective heat transfer coefficient between the windy sky air and the roof surface is 20 $\mathrm{W / ( m^{2} \cdot K )}$. Assuming good insulation below the metal sheet, determine the temperature of the metal sheet

Options:
A. $$
5 6. 4 8^{0} C
$$
B. $$
5 2. 7 1^{0} C
$$
C. $$
4 7. 6 8^{0} C
$$
D. $$
4 9. 2 9^{0} C
$$
E. $$
5 8. 5 3^{0} C
$$
F. $$
5 4. 9 0^{0} C
$$
G. $$
5 9. 7 4^{0} C
$$
H. $$
6 0. 1 3^{0} C
$$
I. $$
4 8. 3 2^{0} C
$$
J. $$
5 3. 5 6^{0} C
$$
Answer: J
According to the steel ball model of the crystal, if the diameter of the ball remains unchanged, based on X-ray diffraction measurements, at 912°C, the lattice parameter of α-Fe is \( $a = 0.2892 \ \mathrm{nm}$ \), and for γ-Fe, it is \( $a = 0.3633 \ \mathrm{nm}$ \). What is the volume expansion when γ-Fe transforms into α-Fe?

Options:
A. 0.56%
B. 0.45%
C. 0.92%
D. 0.34%
E. 1.24%
F. 0.67%
G. 1.15%
H. 0.87%
I. 0.78%
J. 1.03%
Answer: H
Polypropylene is formed by the polymerization of propylene, with its chemical formula being $\mathrm{C_{3}H_{6}}$. Crystalline polypropylene belongs to the monoclinic crystal system, with lattice constants $a=0.665\, \mathrm{nm}, \, b=2.096\, \mathrm{nm}, \, c=0.65\, \mathrm{nm}, \, \alpha=\gamma=90^{\circ}, \, \beta=99.3^{\circ}$. Its density is $\rho=0.91\, \mathrm{g/cm^{3}}$. How many C and H atoms are present in the unit cell of crystalline polypropylene?

Options:
A. 30,60
B. 38,76
C. 33,66
D. 31,62
E. 37,74
F. 39,78
G. 32,64
H. 34,68
I. 36,72
J. 35,70
Answer: J
The subH atom can occupy the interstitial positions in $\alpha-\mathrm{Fe}$. If there is one hydrogen atom for every 200 iron atoms, what are the theoretical and actual packing efficiencies of α-Fe? (Given that for α-Fe, $a = 0.286 \, \mathrm{nm}$, $r_{\mathrm{Fe}} = 0.1241\, \mathrm{nm}$, $r_{\mathrm{H}} = 0.036 \, \mathrm{nm}$).

Options:
A. 0.6854,0.6855
B. 0.6844,0.6845
C. 0.6837,0.6836
D. 0.6835,0.6834
E. 0.6846,0.6847
F. 0.6840,0.6841
G. 0.6852,0.6853
H. 0.6847,0.6848
I. 0.6850,0.6851
J. 0.6839,0.6838
Answer: B
The lattice constant of a known Cu crystal is $a=0.35 \mathrm{~nm}$, and the shear modulus is $G=4 \times 10^{4}$ MPa. There is a dislocation $b={\frac{a} {2}} \left[ \, \overline{{1}} \, 0 \, 1 \, \right]$, with a dislocation line direction of $\left[ \overline{{{1}}} 0 1 \right]$
. What is the strain energy of this dislocation?

Options:
A. $$
3. 9 1 6 \times1 0^{-9} ( \mathrm{N \cdot m / m} )
$$
B. $$
3. 9 6 7 \times1 0^{-9} ( \mathrm{N \cdot m / m} )
$$
C. $$
3. 4 1 5 \times1 0^{-9} ( \mathrm{N \cdot m / m} )
$$
D. $$
3. 5 2 8 \times1 0^{-9} ( \mathrm{N \cdot m / m} )
$$
E. $$
3. 5 3 8 \times1 0^{-9} ( \mathrm{N \cdot m / m} )
$$
F. $$
3. 4 0 9 \times1 0^{-9} ( \mathrm{N \cdot m / m} )
$$
G. $$
3. 0 2 5 \times1 0^{-9} ( \mathrm{N \cdot m / m} )
$$
H. $$
2. 3 7 4 \times1 0^{-9} ( \mathrm{N \cdot m / m} )
$$
I. $$
3. 2 4 1 \times1 0^{-9} ( \mathrm{N \cdot m / m} )
$$
J. $$
3. 8 3 2 \times1 0^{-9} ( \mathrm{N \cdot m / m} )
$$
Answer: C
Which of the following is the effect of molecular chain compliance and molecular weight on viscoflow temperature?

Options:
A. The greater the rigidity of the molecular chain, the lower the viscous flow temperature; the smaller the molecular weight, the higher the viscous flow temperature.
B. The smaller the flexibility of the molecular chain, the higher the viscous flow temperature; the larger the molecular weight, the lower the viscous flow temperature.
C. The greater the rigidity of the molecular chain, the lower the viscous flow temperature; the larger the molecular weight, the lower the viscous flow temperature.
D. The smaller the flexibility of the molecular chain, the higher the viscous flow temperature; the smaller the molecular weight, the lower the viscous flow temperature.
E. The greater the flexibility of the molecular chain, the higher the viscous flow temperature; the smaller the molecular weight, the lower the viscous flow temperature.
F. The smaller the flexibility of the molecular chain, the lower the viscous flow temperature; the larger the molecular weight, the higher the viscous flow temperature.
G. The greater the flexibility of the molecular chain, the higher the viscous flow temperature; the larger the molecular weight, the lower the viscous flow temperature.
H. The greater the rigidity of the molecular chain, the higher the viscous flow temperature; the larger the molecular weight, the lower the viscous flow temperature.
I. The greater the flexibility of the molecular chain, the lower the viscous flow temperature; the larger the molecular weight, the higher the viscous flow temperature.
J. The smaller the flexibility of the molecular chain, the lower the viscous flow temperature; the smaller the molecular weight, the higher the viscous flow temperature.
Answer: I
The relationship between flow stress and dislocation density $\rho$ during plastic deformation of FCC and BCC metals is given by $\tau=\tau_{0}+a G b \, \sqrt{\rho}$, where $\tau_{0}$ is the stress required to move dislocations in the absence of obstacles, which is also the shear stress required when there is no work hardening. $G$ is the shear modulus, and $b$ is the Burgers vector of the dislocation. $\alpha$ is a constant related to the material, with $\alpha=0.3 \sim 0.5$. In fact, this formula also serves as a quantitative relationship for the strengthening effect of work hardening. If for a copper (Cu) single crystal $\tau_{0}=700 \mathrm{~kPa}$, and the initial dislocation density $\rho_{0} = 10^{5} \mathrm{~cm^{-2}}$, what is the critical resolved shear stress?

Options:
A. $$
6 2. 5 0 ( \mathrm{M P a} )
$$
B. $$
1 1. 4 2 ( \mathrm{M P a} )
$$
C. $$
1 0. 8 0 ( \mathrm{M P a} )
$$
D. $$
1 2. 3 5 ( \mathrm{M P a} )
$$
E. $$
8 5. 9 0 ( \mathrm{M P a} )
$$
F. $$
1 5. 2 4 ( \mathrm{M P a} )
$$
G. $$
7 7. 4 8 ( \mathrm{M P a} )
$$
H. $$
9 9. 6 5 ( \mathrm{M P a} )
$$
I. $$
1 3. 8 1 ( \mathrm{M P a} )
$$
J. $$
1 4. 7 5 ( \mathrm{M P a} )
$$
Answer: C
The known H7O brass $\left[w(Zn)=30\%\right]$ completes recrystallization in 1 hour at a constant temperature of 400°C, while at 390°C, it completes recrystallization in 2 hours. Try to calculate how much time is needed to complete recrystallization at a constant temperature of 420°C?

Options:
A. $0.34(h)$
B. $0.28(h)$
C. $0.19(h)$
D. $0.35(h)$
E. $0.30(h)$
F. $0.52(h)$
G. $0.40(h)$
H. $0.45(h)$
I. $0.22(h)$
J. $0.26(h)$
Answer: J
Assuming we add $w \left( \mathrm{Na_{2}O} \right) = 10\%$ of $\mathrm{Na}_{2}O$ to $\mathrm{SiO}_{2}$, please calculate the ratio of oxygen to silicon. If $O : \mathrm{Si} \leqslant 2.5$ is the criterion for vitrification tendency, what is the maximum amount of $\mathrm{Na}_{2}O$ that can form a glass?

Options:
A. 2/7
B. 2/5
C. 3/4
D. 1/3
E. 1/4
F. 5/13
G. 5/12
H. 3/5
I. 1/5
J. 1/6
Answer: D
0.1% carbon (by weight) low-carbon steel is placed in a 1.2% carbon (by weight) carburizing atmosphere for carburization at 920°C. If the carbon content is required to be 0.45% carbon (by weight) at a depth of 0.2 cm from the surface, how much carburizing time is needed? Given that the diffusion activation energy of carbon in austenite (γ-Fe) at 920°C is 133,984 J/mol and $D_{0}=0.71) = 0.68$.

Options:
A. $13.2(h)$
B. $22.0(h)$
C. $17.7(h)$
D. $21.5(h)$
E. $19.1(h)$
F. $15.3(h)$
G. $14.8(h)$
H. $16.9(h)$
I. $20.3(h)$
J. $18.5(h)$
Answer: C
The yield strength of industrial pure copper is known to be $\sigma_{\mathrm{S}}=70 \mathrm{~MPa}$, with a grain size of $N_{\mathrm{A}}=18 \uparrow/\mathrm{mm}^{2}$. When $N_{\mathrm{A}}=4025 \text{ grains/mm}^2$, $\sigma_{\mathrm{s}}=95 \mathrm{~MPa}$. When $N_{\mathrm{A}}=4025 \text{ grains/mm}^2$, $\sigma_{\mathrm{s}}=95 \mathrm{~MPa}$, the $\sigma_{\mathrm{s}}$ is ____ when $N_{\mathrm{A}}=260 \text{ grains/mm}^2$.

Options:
A. $$
6 5. 2 ( \mathrm{M P a} )
$$
B. $$
9 0. 1 ( \mathrm{M P a} )
$$
C. $$
7 2. 9 ( \mathrm{M P a} )
$$
D. $$
8 5. 0 ( \mathrm{M P a} )
$$
E. $$
7 8. 3 ( \mathrm{M P a} )
$$
F. $$
8 2. 7 ( \mathrm{M P a} )
$$
G. $$
9 3. 5 ( \mathrm{M P a} )
$$
H. $$
7 6. 4 ( \mathrm{M P a} )
$$
I. $$
7 1. 8 ( \mathrm{M P a} )
$$
J. $$
8 0. 6 ( \mathrm{M P a} )
$$
Answer: E
In the Compton scattering experiment, when the wavelength of the incident light is 0.050 nm X-rays and 500 nm visible light, what is the maximum energy acquired by the recoil electrons?

Options:
A. $$
E_{k_{1}}=2. 6 \mathrm{k e V},
$$
$$
E_{k_{2}}=3. 3 \, \times\, 1 0^{-5} \mathrm{e V}
$$
B. $$
E_{k_{1}}=2. 1 \mathrm{k e V},
$$
$$
E_{k_{2}}=2. 8 \, \times\, 1 0^{-5} \mathrm{e V}
$$
C. $$
E_{k_{1}}=1. 7 \mathrm{k e V},
$$
$$
E_{k_{2}}=2. 7 \, \times\, 1 0^{-5} \mathrm{e V}
$$
D. $$
E_{k_{1}}=2. 0 \mathrm{k e V},
$$
$$
E_{k_{2}}=3. 2 \, \times\, 1 0^{-5} \mathrm{e V}
$$
E. $$
E_{k_{1}}=2. 2 \mathrm{k e V},
$$
$$
E_{k_{2}}=2. 4 \, \times\, 1 0^{-5} \mathrm{e V}
$$
F. $$
E_{k_{1}}=2. 4 \mathrm{k e V},
$$
$$
E_{k_{2}}=2. 9 \, \times\, 1 0^{-5} \mathrm{e V}
$$
G. $$
E_{k_{1}}=2. 3 \mathrm{k e V},
$$
$$
E_{k_{2}}=2. 6 \, \times\, 1 0^{-5} \mathrm{e V}
$$
H. $$
E_{k_{1}}=1. 8 \mathrm{k e V},
$$
$$
E_{k_{2}}=3. 1 \, \times\, 1 0^{-5} \mathrm{e V}
$$
I. $$
E_{k_{1}}=2. 5 \mathrm{k e V},
$$
$$
E_{k_{2}}=3. 0 \, \times\, 1 0^{-5} \mathrm{e V}
$$
J. $$
E_{k_{1}}=1. 9 \mathrm{k e V},
$$
$$
E_{k_{2}}=2. 5 \, \times\, 1 0^{-5} \mathrm{e V}
$$
Answer: E
Calculate the de Broglie wavelength of an electron using both relativistic and non-relativistic approaches. At what kinetic energy does the discrepancy between the two calculations reach 5%?

Options:
A. $$
0. 3 5 0 \mathrm{M e V}
$$
B. $$
0. 1 5 0 \mathrm{M e V}
$$
C. $$
0. 4 0 0 \mathrm{M e V}
$$
D. $$
0. 2 5 0 \mathrm{M e V}
$$
E. $$
0. 0 7 0 \mathrm{M e V}
$$
F. $$
0. 1 0 5 \mathrm{M e V}
$$
G. $$
0. 0 5 0 \mathrm{M e V}
$$
H. $$
0. 1 2 5 \mathrm{M e V}
$$
I. $$
0. 0 9 0 \mathrm{M e V}
$$
J. $$
0. 2 0 0 \mathrm{M e V}
$$
Answer: F
Assume that a portion of the hydrogen isotope with a mass number of 3 (tritium) is introduced into a discharge tube containing normal hydrogen gas, reaching a level sufficient for observation with a spectrometer. Determine the spacing of the first line of the Balmer series to be observed (expressed as a wavelength difference) is ().

Options:
A. $$
\lambda_{3_{\mathrm{T}}}-\lambda_{2_{\mathrm{H}}}=0.37(nm)
$$
B. $$
\lambda_{1_{\mathrm{H}}}-\lambda_{3_{\mathrm{H}}}=0.24(nm)
$$
C. $$
\lambda_{1_{\mathrm{T}}}-\lambda_{2_{\mathrm{D}}}=0.32(nm)
$$
D. $$
\lambda_{2_{\mathrm{H}}}-\lambda_{1_{\mathrm{T}}}=0.15(nm)
$$
E. $$
\lambda_{1_{\mathrm{H}}}-\lambda_{2_{\mathrm{T}}}=0.51(nm)
$$
F. $$
\lambda_{1_{\mathrm{D}}}-\lambda_{2_{\mathrm{H}}}=0.73(nm)
$$
G. $$
\lambda_{2_{\mathrm{T}}}-\lambda_{3_{\mathrm{H}}}=0.66(nm)
$$
H. $$
\lambda_{2_{\mathrm{H}}}-\lambda_{3_{\mathrm{T}}}=0.48(nm)
$$
I. $$
\lambda_{1_{\mathrm{D}}}-\lambda_{3_{\mathrm{H}}}=0.89(nm)
$$
J. $$
\lambda_{3_{\mathrm{H}}}-\lambda_{1_{\mathrm{H}}}=0.19(nm)
$$
Answer: B
What is the energy of the photon emitted during the transition of a carbon-$\mu$ atom from $n=3$ to $n=2$? (Expressed in terms of the energy of the photon emitted during the electron transition in a hydrogen atom from $n=2$ to $n=1$) Given $m_{\mu} / m_{\mathrm{e}} = 207$.

Options:
A. $$
1 5 9 2 \big[ E_{1} ( \mathrm{H} )-E_{3} ( \mathrm{H} ) \big]
$$
B. $$
1 6 5 4 \big[ E_{2} ( \mathrm{H} )-E_{1} ( \mathrm{H} ) \big]
$$
C. $$
1 2 8 0 \big[ E_{3} ( \mathrm{H} )-E_{2} ( \mathrm{H} ) \big]
$$
D. $$
1 3 8 0 \big[ E_{2} ( \mathrm{H} )-E_{3} ( \mathrm{H} ) \big]
$$
E. $$
1 2 5 0 \big[ E_{3} ( \mathrm{H} )-E_{2} ( \mathrm{H} ) \big]
$$
F. $$
1 3 8 0 \big[ E_{1} ( \mathrm{H} )-E_{2} ( \mathrm{H} ) \big]
$$
G. $$
1 3 5 0 \big[ E_{2} ( \mathrm{H} )-E_{1} ( \mathrm{H} ) \big]
$$
H. $$
1 3 8 0 \big[ E_{3} ( \mathrm{H} )-E_{1} ( \mathrm{H} ) \big]
$$
I. $$
1 7 8 0 \big[ E_{2} ( \mathrm{H} )-E_{1} ( \mathrm{H} ) \big]
$$
J. $$
1 3 8 0 \big[ E_{2} ( \mathrm{H} )-E_{1} ( \mathrm{H} ) \big]
$$
Answer: J
For a certain type of hydrogen ion, the first line of the Lyman series is composed of two lines with a wavenumber difference of $228.40 \, \mathrm{cm}^{-1}$. What kind of hydrogen ion is it?

Options:
A. 5.00; is a doubly excited oxygen ion.
B. 5.00; is a quadruply excited sulfur molecule.
C. 5.00; is a quadruply ionized boron ion.
D. 5.00; is a quadruply excited lithium ion.
E. 5.00; is a doubly ionized hydrogen molecule.
F. 5.00; is a triple-ionized neon atom.
G. 5.00; is a triple-ionized nitrogen atom.
H. 5.00; is a doubly ionized argon atom.
I. 5.00; is a quadruply ionized helium ion.
J. 5.00; is a singly excited carbon atom.
Answer: C
A particle with a spin $s = 1/2$ has a magnetic moment $\mu = \mu_{\mathrm{B}} s$ and is placed in a constant magnetic field $B$ along the $x$ direction. At time $t = 0$, the particle is in the $s_{z} = 1/2$ state. Determine the probability that the particle is subsequently found in the $s_{y} = \pm 1/2$ state.

Options:
A. $$
{\frac{1} {3}} \Bigl( 1+\operatorname{s i n} {\frac{\mu_{\mathrm{B}} B t} {h}} \Bigr)
$$
$$
{\frac{1} {3}} \Bigl( 1-\operatorname{s i n} {\frac{\mu_{\mathrm{B}} B t} {h}} \Bigr) \,.
$$
B. $$
{\frac{1} {2}} \Bigl( 1+\operatorname{s i n} {\frac{\mu_{\mathrm{B}} B t} {2h}} \Bigr)
$$
$$
{\frac{1} {2}} \Bigl( 1-\operatorname{s i n} {\frac{\mu_{\mathrm{B}} B t} {2h}} \Bigr) \,.
$$
C. $$
{\frac{1} {2}} \Bigl( 1-\operatorname{cos} {\frac{\mu_{\mathrm{B}} B t} {h}} \Bigr)
$$
$$
{\frac{1} {2}} \Bigl( 1+\operatorname{cos} {\frac{\mu_{\mathrm{B}} B t} {h}} \Bigr) \,.
$$
D. $$
{\frac{1} {5}} \Bigl( 1+\operatorname{s i n} {\frac{\mu_{\mathrm{B}} B t} {h}} \Bigr)
$$
$$
{\frac{1} {5}} \Bigl( 1-\operatorname{s i n} {\frac{\mu_{\mathrm{B}} B t} {h}} \Bigr) \,.
$$
E. $$
{\frac{1} {2}} \Bigl( 1+\operatorname{tan} {\frac{\mu_{\mathrm{B}} B t} {h}} \Bigr)
$$
$$
{\frac{1} {2}} \Bigl( 1-\operatorname{tan} {\frac{\mu_{\mathrm{B}} B t} {h}} \Bigr) \,.
$$
F. $$
{\frac{1} {2}} \Bigl( 1+\operatorname{s i n} {\frac{2\mu_{\mathrm{B}} B t} {h}} \Bigr)
$$
$$
{\frac{1} {2}} \Bigl( 1-\operatorname{s i n} {\frac{2\mu_{\mathrm{B}} B t} {h}} \Bigr) \,.
$$
G. $$
{\frac{1} {4}} \Bigl( 1+\operatorname{s i n} {\frac{\mu_{\mathrm{B}} B t} {h}} \Bigr)
$$
$$
{\frac{1} {4}} \Bigl( 1-\operatorname{s i n} {\frac{\mu_{\mathrm{B}} B t} {h}} \Bigr) \,.
$$
H. $$
{\frac{3} {2}} \Bigl( 1+\operatorname{s i n} {\frac{\mu_{\mathrm{B}} B t} {h}} \Bigr)
$$
$$
{\frac{3} {2}} \Bigl( 1-\operatorname{s i n} {\frac{\mu_{\mathrm{B}} B t} {h}} \Bigr) \,.
$$
I. $$
{\frac{1} {2}} \Bigl( 1+\operatorname{s i n} {\frac{\mu_{\mathrm{B}} B t} {h}} \Bigr)
$$
$$
{\frac{1} {2}} \Bigl( 1-\operatorname{s i n} {\frac{\mu_{\mathrm{B}} B t} {h}} \Bigr) \,.
$$
J. $$
{\frac{1} {2}} \Bigl( 1+\operatorname{cos} {\frac{2\mu_{\mathrm{B}} B t} {h}} \Bigr)
$$
$$
{\frac{1} {2}} \Bigl( 1-\operatorname{cos} {\frac{2\mu_{\mathrm{B}} B t} {h}} \Bigr) \,.
$$
Answer: I