Solved Examples on Power of a Nuclear ReactorNuclear Reactor is an important topic of IIT JEE syllabus. The topic is quite simple and easily fetches 3-4 questions in the JEE. With a bit of hard work it becomes easy to master this topic and in fact, it is vital to have a good hold on it to remain competitive in the IIT JEE. The questions asked in JEE may range from the simple ones like estimating number of fissions per second to difficult ones like the nuclear power calculation. Some sample problems with solution of nuclear energy fission and fusion and on nuclear reactor have been discussed here:

1. The mass number of a nucleus is(A) Always less than atomic number

(B) Always more than atomic number

(C) Equal to atomic number

(D) Some times more than and sometimes equal to atomic number.

Solution: We know that the mass number of a nucleusrepresents the number of nucleons (neutrons + protons), and the atomic number represents the number of neutrons in the nucleus. So, when there are no neutrons in the nucleus, only then the atomic number equals the mass number. Hence, the correct option is (D).2

. In which of the following decays, the element does not change?(A) β – decay (B) α – decay

(C) Positive– decay (D) γ – decay

Solution: We know thatγ ray has no charge and no mass. Hence, it is during the emission of γ ray that there is no change in atomic number or mass number. So, the correct option is (D).Watch this video to view more on alpha and beta rays3

(A) 1.21 MeV (B) 1.62 MeV. In the reaction_{7}N^{14}+_{2}He^{4}—>_{8}O^{17}+_{1}H^{1}the minimum energy of the α-particle is

(C) 1.89 MeV (D) 1.96 MeV.

(M_{N}= 14.00307 amu, M_{He}= 4.00260 amu and M_{O}

= 16.99914 amu, M_{H}= 1.00783 amu and 1 amu = 931 MeV)Solution: The given reaction is_{7}N^{14}+_{2}He^{4}—>_{8}O^{17}+_{1}H^{1}

We first calculate the total mass of reactants as well as products

Total mass of reactants = 18.00567 amu

Total mass of products = 18.00697 amu

Mass defect = 18.00697 – 18.00567 = 0.0013 amu

Energy (E) = 931 (0.0013) = 1.2103 MeV

Hence the correct option is (A).4. In the carbon cycle of fusion

(A) Four_{1}H^{1}fuse to form_{2}He^{4 }and two positrons

(B) Four_{ 1}H^{1}fuse to form_{2}He^{4 }and two electrons

(C) Two_{1}H^{2}fuse to form_{2}He^{4}

(D) Two_{1}H^{2}fuse to form_{ 2}He^{4 }and two neutronsSolution: The carbon cycle of fusion is given by this equation

4^{1}H^{1}—>_{2}He^{4}+ 2._{+1}e^{0}+ Energy

Hence, it is clear that in this equation four_{1}H^{1}fuse to form_{2}He^{4 }and two positrons. So, (A) is the correct option.(A) 3.125 × 10

5. In each fission of U^{235}, 200 MeV of energy is released. If a reactor produces 100 MW power, then the rate of fission in it will be^{18}per minute

(B) 3.125 × 10^{17}per second

(C) 3.125 × 10^{17}per minute

(D) 3.125 × 10^{18}per secondSolution: The energy released in every fission ofUP = nE/t.^{235 }is given in the question. We know the formula

Hence, substituting the values in this formula, we get

n/t = P/E = 100×10^{6}/ 200[1.6×10^{13}]

= 3.125 × 10^{18}/sec

SO (D) is the correct option.

6. To generate a power of 3.2 MW, the number of fissions of U^{235}per minute is (Energy released per fission = 200 MeV, 1 eV = 1.6 ´ 10^{–19}J)

(A) 6×10^{18}¡ (B) 6×10^{17}

(C) 10^{17}(D) 6×10^{16}Solution: The power of reactor P = nE/tHere, ‘n’ denotes the number of fissions,‘t’ denotes the time and ‘E’ is the energy released per fission.

∴ 3.2 × 10^{6}= n(200×10^{6})(1.6×10^{–19}) / 60

=> n = 6 × 10^{18}. This gives (A) as the correct option.

7. If in nuclear reactor using U^{235}as fuel, the power output is 4.8 MW, the number of fissions per second is (Energy released per fission of U^{235}= 200 MeV watts, e eV = 1.6 ´ 10^{–19}J)

(A) 1.5×10^{17 }(B) 3×10^{19}

(C) 1.5×0^{25}(D) 3×10^{25}Solution: The power output is given to be4.8 MW. This may be represented as

P = 4.8 MW = 4.8×10^{6}W

The power of a nuclear reactor is given by the formula P = nE/t

∴ n/t = P/E = 4.8×10^{6}/ (200)(1.6×10^{–13}) = 1.5 × 10^{17}

So this gives (A) as the correct option.It is vital for the JEE aspirants to master this topic and practice nuclear fission problems solutions. askIITians offers solved problems about nuclear reaction and nuclear reaction examples.

Related resources:

- Click here for the Detailed IIT JEE Physics Syllabus.
- Get an idea about the kinds of questions asked by referring the Model Papers of Previous Years.
- You can know the Recommended Books of Physics here.