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 ______.

JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Modern Physics

Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous

α

-decay with same Q value of 1 MeV . The ratio of energies of

α

-rays produced by A and

B

is ______.

(A) $\frac{2548}{2650}$
(B) $\frac{2706}{2646}$
(C) $\frac{2597}{2600}$ ✓ Correct
(D) $\frac{2862}{2499}$

Answer: (C)

Solution

When a nucleus of mass number

A

emits an

α

particle, momentum conservation shares the released energy so that the

α

particle carries

K_{α} = \frac{A - 4}{A} Q

. For A,

K_{α} = \frac{196}{200} Q

; for B,

K_{α} = \frac{208}{212} Q

. With equal

Q

, the ratio is

\frac{196/200}{208/212} = \frac{196 \times 212}{200 \times 208} = \frac{41552}{41600} = \frac{2597}{2600}

. The ratio of

α

-ray energies of A and B is

\frac{2597}{2600}

JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Single correct option

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