Practice Nuclear Physics MCQ with Answers.

**Nuclear Physics MCQ with Answer**

**Q1. ^{238}U decays with a half life of 4.51 × 100 years, the decay series eventually ending at ^{206}Pb, which is stable. A rock sample analysis shows that the ratio of the numbers of atoms of ^{206}Pb to ^{238}U is 0.0058. Assuming that all the ^{206}Pb has been produced by the decay of ^{238}U and that all other half-lives in the chain are negligible, the age of the rock sample is**

(a) 38 × 10^{6} years

(b) 48 × 10^{6} years

(c) 38 × 10^{7} years

(d) 48 × 10^{7} years

**Q2. The binding energy of the k-shell electron in a Uranium atom (Z = 92, A = 238) will be modified due to (i) screening caused by other electrons and (ii) the finite extent of the nucleus as follows:**

(a) increascs due to (i), remains unchanged due to (i)

(b) decreases due to (i), decreases due to (ii).

(c) increases due to (i), increases due to (i).

(d) decreases due to (i), remains unchanged due to (i).

**Q3. In the mixture of isotopes normally found on the earth at the present time, _{92}U^{238} has an abundance of 99.3% and _{92}U^{235} has an abundance of 0.7%. The measured lifetimes of these isotopes are 6.52 × 10^{9} years and 1.02 × 10^{9} years, respectively. Assuming that they were equally abundant when the earth was formed, the estimated age of the earth, in years, is**

(a) 6.0 × 10^{9}

(b) 1.0 × 10^{9}

(c) 6.0 × 10^{8}

(d) 1.0 × 10^{8}

**Q4. The hale-life of a radioactive nuclear source is 9 days. The fraction of nuclei which are let undecayed after 3 days is**

(a) ^{7}/_{8}

(b) ^{1}/_{3}

(c) ^{5}/_{6}

(d) ^{1}/_{21/3}

**Q5. An alpha particle of energy E is shot towards a gold nucleus ( _{79}Au^{197}). At the distances much larger than the nuclear size R_{N}, the dominant force is the Coulomb repulsion, but at distances comparable to the nuclear size the dominant force is the strong nuclear attraction. These combine to form a potential barrier of height V_{c} .If E < V_{c} the probability that the alpha particle will fuse with the gold nucleus can be written (in terms of a dimensionless positive constant k) as**

(a) Zero

(b) ^{kE}/_{√[k2E2 + (Vc)2]}

(c) k(1-^{E}/_{Vc})

(d) exp(-kVc/_{E})

**Q6. It is well-known that the energy of the Sun arises from the fusion of hydrogen nuclei (protons) inside the core of the Sun. This takes place through several mechanisms, each resulting in emission of energy. Which of the following reactions is NOT possible during the proton fusion inside the Sun?**

(a) _{1}H^{1} + _{1}H^{1}→ _{2}He^{2}

(b) _{1}H^{2} + _{1}H^{1}→ _{2}He^{3}

(c) _{1}H^{1} + _{1}H^{1} → _{1}He^{2} + e^{+} +v_{e}

(d) _{1}H^{1} + _{1}H^{1} + _{1}H^{1} + _{1}H^{1} → _{1}He^{4} + 2e^{+}

**Q7. Consider a process in which atoms of Actinium-226 ( _{89}Ac^{226) }get converted to atoms of Radium-226 (_{88}Ra^{226}) and the yield of energy is 0.64 MeV per atom. This occurs through**

(a) Both p → n + e^{+} + v_{e} and p + e^{–} → n + v_{e}

(b) Both p → n + e^{+} + v_{e} and n → p + e^{–} + v’_{e}

(c) Only p → n + e^{+} + v_{e}

(d) Only p + e^{–} → n + v_{e}

**Q8. The binding energy per nucleon for ^{235}U is 7.6 MeV. The ^{235}U nucleus undergoes fission to produce two fragments, both having binding energy per nucleon 8.5 MeV. the energy released, in Joules, from the complete fission of 1 kG of ^{235}U is therefore,**

(a) 10^{13}

(b) 7.7 × 10^{13}

(c) 5 × 10^{8}

(d) 8.7 x 10^{13}

**Q9. Two spherical nuclei have mass numbers 216 and 64 with their radii R _{1} and R_{2} respectively. The ratio R_{1}/R_{2} is**

(a) 1.0

(b) 1.5

(c) 2.0

(d) 2.5

**Q10. A proton is accelerated to a high energy E and shot at a nucleus of Oxygen ( _{8}O^{16}) . In order to penetrate the Coulomb barrier and reach the surface of the Oxygen nucleus, E must be at least**

(a) 3.6 MeV

(b) 1.8 MeV

(c) 45 keV

(d) 180 eV

**Q11. In a nuclear reactor, Plutonium ( _{94}Pu^{239}) is used as fuel, releasing energy by its fission into isotopes of Barium (_{54}Ba^{146}) and Strontium (_{38}Sr^{91}) through the reaction**

_{94}Pu^{239} + _{0}n^{1} → _{56}Ba^{146} + _{38}Sr^{91} +3 × _{0}n^{1}

**The binding energy (B.E.) per nucleon of each of these nuclides is given in the table below:**

Nuclide | _{94}Pu^{239} | _{56}Ba^{146} | _{38}Sr^{91} |

B.E. per nucleon (MeV) | 7.6 | 8.2 | 8.6 |

**Using this information, one can estimate the number of such fission reactions per second in a 100MW reactor as**

(a) 3.9 × 10^{18}

(b) 7.8 × 10^{18}

(c) 5.2 × 10^{18}

(d) 5.2 × 10^{18}

**Q12. Let E _{N} be the energy released when one mole of pure ^{235}U undergoes controlled fission, and E_{c} be the energy released when one mole of pure carbon undergoes complete combustion. The ratio E_{N}/_{Ec} will have the order of magnitude**

(a) 10^{4}

(b) 10^{8}

(c) 10^{9}

(d) 10^{6}

**Q13. A particle P, of rest mass M and energy E, suddenly decays into two particles A and B of rest masses m _{A} and m_{B} respectively, and both particles move along the straight line in which P was moving, A possible energy E_{A} of the particle A will be**

(a) ^{E}/_{2} [1 + {(m_{A} – m_{B})/_{M}}^{2}]

(b) ^{E}/_{2} [1 – {(m^{2}_{A} – m^{2}_{B})/_{M2}}^{2}]

(c) ^{E}/_{2} [1 + {(m_{A} + m_{B})/_{M}}^{2}]

(d) ^{E}/_{2} [1 + {(m^{2}_{A} – m^{2}_{B})/_{M2}}^{2}]

**Q14. If M _{e}, M_{p}, and M_{H} are the rest masses of electron, proton and hydrogen atom in the ground state (with energy -13.6 eV), respectively, which of the following is exactly true? (c is the speed of light in free space)**

(a) M_{H} = M_{p} + M_{e}

(b) M_{H} = M_{p} + M_{e} – ^{13.6 eV}/_{c2},

(c) M_{H} = M_{p} + M_{e} + ^{13.6 eV}/_{c2}

(d) M_{H} = M_{p} + M_{e} + K, where K ≠ ^{13.6 eV}/_{c2 }or zero.

**Q15.The activity of a radioactive sample is decreased to 75% of the initial value after 30 days. The half-life (in days) of the sample is approximately [You may use In3 ≈ 1.1, In 4 ≈ 1.4]**

(a) 38

(b) 45

(c) 59

(d) 69

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*Answer Key* (if you find any answer wrong, feel free to Correct us)

*Answer Key*

01. | (a) | 06. | (d) | 11. | (a) |

02. | (b) | 07. | (d) | 12. | (d) |

03. | (a) | 08. | (d) | 13. | (d) |

04. | (d) | 09. | (b) | 14. | (b) |

05. | (d) | 10. | (a) | 15. | (d) |