Training Nuclear Engineering Placement Test Practice — Nuclear Engineering
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Placement Test Practice — Nuclear Engineering

25 min Nuclear Engineering

Placement Test Practice — Nuclear Engineering

This practice test covers all major topics in nuclear engineering mathematics: radioactive decay, binding energy, chain reactions, neutron diffusion, radiation shielding, and reactor thermal hydraulics. Work through each problem carefully, showing all steps. These problems integrate concepts from multiple lessons and require you to identify which formula applies, set up the calculation, and interpret the physical meaning of your answer.

Practice Test

1. Cesium-137 ($t_{1/2} = 30.17$ yr) contaminated a region after a reactor accident. How long until the activity drops to 1/1000 of its original value?
2. Calculate the energy released in the fission of U-235 into Ba-141 and Kr-92 plus 3 neutrons. (Masses: U-235 = 235.0439 u, n = 1.00867 u, Ba-141 = 140.9144 u, Kr-92 = 91.9262 u)
3. A reactor operates with $\eta = 2.08$, $\varepsilon = 1.03$, $p = 0.75$, $f = 0.90$, $P_{NL} = 0.93$. Find $k_{\text{eff}}$ and the reactivity in pcm.
4. A slab reactor with $\tilde{a} = 350$ cm has $\phi_{\max} = 2 \times 10^{14}$ n/cm²·s. Find the flux at 60 cm from center and the average flux.
5. A shield uses 30 cm of lead ($\mu = 0.12$ cm$^{-1}$) backed by 50 cm of concrete ($\mu = 0.06$ cm$^{-1}$). What is the total attenuation factor?
6. A 2000 MWth BWR has $\eta = 33\%$. If coolant $c_p = 4800$ J/kg·K and $\Delta T = 28°$C, find the mass flow rate and electrical output.
7. Plutonium-239 has $t_{1/2} = 24{,}110$ yr. A weapons pit contains 4 kg. Find the activity in curies. ($M_{Pu} = 239$ g/mol, $N_A = 6.022 \times 10^{23}$)
8. At $k_{\text{eff}} = 1.0005$ (slightly supercritical), how many generations for neutron population to increase by 10%?
9. Design problem: a medical linear accelerator room needs shielding to reduce 10 MeV photon dose from 5000 mSv/hr to 0.01 mSv/hr at the wall. If concrete HVL is 10 cm, what wall thickness is required?
10. A submarine reactor produces 150 MWth using seawater cooling ($c_p = 3900$ J/kg·K, $\Delta T = 20°$C). Find $\dot{m}$ and discuss the engineering challenge of operating underwater.
Show Answer Key

1. $0.001 = (1/2)^{t/30.17}$. $t/30.17 = \log_2(1000) = 9.97$. $t = 9.97 \times 30.17 = 300.6$ years.

2. Reactants: $235.0439 + 1.00867 = 236.0526$ u. Products: $140.9144 + 91.9262 + 3(1.00867) = 235.8667$ u. $\Delta m = 0.1859$ u. $E = 0.1859 \times 931.5 = 173.2$ MeV. (The remaining ~27 MeV comes from neutrinos and fission product decay.)

3. $k_\infty = 2.08 \times 1.03 \times 0.75 \times 0.90 = 1.446$. $k_{\text{eff}} = 1.446 \times 0.93 = 1.345$. $\rho = 0.345/1.345 = 0.2565 = 25{,}650$ pcm. Very supercritical.

4. $\phi(60) = 2 \times 10^{14} \cos(60\pi/350) = 2 \times 10^{14} \cos(0.5386) = 2 \times 10^{14} \times 0.857 = 1.71 \times 10^{14}$. Average $= (2/\pi) \times 2 \times 10^{14} = 1.27 \times 10^{14}$.

5. $I/I_0 = e^{-(0.12 \times 30 + 0.06 \times 50)} = e^{-(3.6+3.0)} = e^{-6.6} \approx 0.00136$. Attenuation factor $\approx 735$.

6. $\dot{m} = 2 \times 10^9/(4800 \times 28) = 14{,}881$ kg/s. $P_e = 0.33 \times 2000 = 660$ MWe.

7. $N = (4000/239) \times 6.022 \times 10^{23} = 1.008 \times 10^{25}$. $\lambda = 0.6931/(24110 \times 3.156 \times 10^7) = 9.11 \times 10^{-13}$ s$^{-1}$. $A = 9.11 \times 10^{-13} \times 1.008 \times 10^{25} = 9.18 \times 10^{12}$ Bq $= 248$ Ci.

8. $1.1 = 1.0005^n$. $n = \ln(1.1)/\ln(1.0005) = 0.09531/0.000500 = 190.6 \approx 191$ generations.

9. Factor $= 5000/0.01 = 500{,}000$. HVLs $= \log_2(500{,}000) = 18.9$. Thickness $= 18.9 \times 10 = 189$ cm $\approx 1.9$ m of concrete.

10. $\dot{m} = 150 \times 10^6/(3900 \times 20) = 1923$ kg/s. Challenges: compact core design, corrosion from seawater, silent operation requirements, limited space for shielding, radiation protection for crew in confined quarters.

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