Q50 / 60 · JEE Advanced 2013 (Paper 2) · Physics

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 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 $M$ can break into two light nuclei of masses $m_{1}$ and $m_{2}$ only if $\left(m_{1}+m_{2}\right) \lt M$. Also two light nuclei of masses $m_{3}$ and $m_{4}$ can undergo complete fusion and form a heavy nucleus of mass $M^{\prime}$ only if $\left(m_{3}+m_{4}\right) \gt M^{\prime}$. The masses of some neutral atoms are given in the table below: Figure
$\left(1 u=932 M e V / c^{2}\right)$
Question: The kinetic energy (in $k e V$ ) of the alpha particle, when the nucleus ${ }_{84}^{210} P o$ at rest undergoes alpha decay, is

  • Correct answer
    A
    5320
  • B
    5422
  • C
    5707
  • D
    5818

Solution

84 Po 210 + 2 He 4 → 82 Pb 206
Δ m = M PO - M He - M Pb = 0.008421 u
Q = 0.008421 × 9 3 2  MeV = 5 4 2 2  KeV
K α = 2 1 0 2 1 4 × 5 4 2 2  KeV = 5 3 2 0  KeV

Hence, the correct answer is option: 'A'.

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