Atoms & Nuclei

JEE Main level, single correct, medium

183 of 239

Question 183 of 239

The binding energy per nucleon of 83209Bi^{209}_{83}Bi is _______ MeV.
[Take m(83209Bi)=208.980388 u, mp=1.007825 u, mn=1.008665 u, 1 u=931 MeV/c2][\text{Take } m(^{209}_{83}Bi) = 208.980388 \, u, \, m_p = 1.007825 \, u, \, m_n = 1.008665 \, u, \, 1 \, u = 931 \, \text{MeV}/c^2]

Show answer and solution

Answer: (B) 7.847.84

For the nucleus 83209Bi^{209}_{83}Bi, the number of protons is Z=83Z = 83 and the number of neutrons is N=209−83=126N = 209 - 83 = 126.

Mass of 8383 protons =83×1.007825=83.649475 u= 83 \times 1.007825 = 83.649475 \, u

Mass of 126126 neutrons =126×1.008665=127.091790 u= 126 \times 1.008665 = 127.091790 \, u

Total mass of the nucleons =83.649475+127.091790=210.741265 u= 83.649475 + 127.091790 = 210.741265 \, u

The mass defect Δm\Delta m is given by:

Δm=Total mass of nucleons−Mass of nucleus\Delta m = \text{Total mass of nucleons} - \text{Mass of nucleus}

Δm=210.741265−208.980388=1.760877 u\Delta m = 210.741265 - 208.980388 = 1.760877 \, u

The total binding energy (BEBE) is:

BE=Δm×931 MeVBE = \Delta m \times 931 \, \text{MeV}

BE=1.760877×931=1639.376 MeVBE = 1.760877 \times 931 = 1639.376 \, \text{MeV}

The binding energy per nucleon is:

BEA=1639.376209≈7.84 MeV\dfrac{BE}{A} = \dfrac{1639.376}{209} \approx 7.84 \, \text{MeV}

Answer: 7.847.84

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Atoms: Rutherford, Bohr and X-rays simulationDrag the sliders and watch the numbers in this question change.Revise Modern Physics firstFormula sheet, solved examples and the traps students fall into.

More Physics practice

JEE Main Physics practice question on Atoms & Nuclei (Nuclear energy), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.