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JEE Advanced 2013Paper 2
Exam
JEE Advanced
Year
2013
Paper
Paper 2
Subject
Physics
Chapter
Nuclear Physics

JEE Advanced 2013 · Paper 2 · Physics · Nuclear Physics

Paragraph: The mass of a nucleus _ Z ^ A X is less than the sum of...

Paragraph: The mass of a nucleus ZAX{ }_{Z}^{A} X is less than the sum of the masses of (A−Z)(A-Z) number of neutrons and ZZ number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass MM can break into two light nuclei of masses m1andm2m_{1} and m_{2} only if (m1+m2)<M\left(m_{1}+m_{2}\right) \lt M. Also two light nuclei of masses m3andm4m_{3} and m_{4} can undergo complete fusion and form a heavy nucleus of mass M′M^{\prime} only if (m3+m4)>M′\left(m_{3}+m_{4}\right) \gt M^{\prime}. The masses of some neutral atoms are given in the table below: Paragraph: The mass of a nucleus _ Z ^ A X is less than the sum of the masses of (A-Z) number of neutrons and Z number
(1u=932MeV/c2)\left(1 u=932 M e V / c^{2}\right)
Question: The kinetic energy (in keVk e V ) of the alpha particle, when the nucleus 84210Po{ }_{84}^{210} P o at rest undergoes alpha decay, is

Options

  1. A53205320
  2. B54225422
  3. C57075707
  4. D58185818

Correct answer

A. 53205320

Step-by-step solution

84Po210+2He4→82Pb206{\text{84}}^{{\text{Po}}^{\text{210}}} + {2}^{{\text{He}}^{4}} \to {\text{82}}^{{\text{Pb}}^{\text{206}}}
Δm=[MPO−MHe−MPb]=0.008421 u\Delta \text{m} = \left[{\text{M}}_{\text{PO}} - {\text{M}}_{\text{He}} - {\text{M}}_{\text{Pb}}\right] = \text{0.008421 u}
Q=0.008421×932MeV=5422KeV\text{Q} = \text{0.008421} \times 9 3 2 \text{MeV} = 5 4 2 2 \text{KeV}
Kα=210214×5422KeV=5320KeV{\text{K}}_{\alpha} = \dfrac{2 1 0}{2 1 4} \times 5 4 2 2 \text{KeV} = 5 3 2 0 \text{KeV}
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