Two radioactive substances A and B of…

Single correct+4 / -1Answer matches NTA’s final key

Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous $\alpha$ -decay with same $Q$ value of 1 MeV. The ratio of energies of $\alpha$ -rays produced by A and B is ______.

$\frac{2548}{2650}$
$\frac{2706}{2646}$
$\frac{2597}{2600}$
$\frac{2862}{2499}$

Solution

The parent is at rest, so the alpha particle and the daughter share momentum equally and kinetic energy in inverse ratio of mass. For a parent of mass number $A$ :

$K_\alpha = Q\,\frac{A - 4}{A}.$

$\frac{K_A}{K_B} = \frac{196/200}{208/212} = \frac{196 \times 212}{200 \times 208} = \frac{41552}{41600} = \frac{2597}{2600}.$

Answer: $\frac{2597}{2600}$ .

Answer checked against the official answer key. The solution is our own working.

JEE MAIN 2026 · Atoms and Nuclei

Solution

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