Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous -decay with same

Question

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 _______. [2026]

Smart Achievers · Accepted Answer

(3)

$K_{α} = (\frac{A - 4}{A}) Q$

${(K_{α})}_{A} = (\frac{196}{200}) Q and {(K_{α})}_{B} = (\frac{208}{212}) Q$

$\frac{{(K_{α})}_{A}}{{(K_{α})}_{B}} = \frac{196 \times 212}{200 \times 208} = \frac{2597}{2600}$

Solution

Q.
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 _______. [2026]

1 $\frac{2548}{2650}$

2 $\frac{2706}{2646}$

3 $\frac{2597}{2600}$

4 $\frac{2862}{2499}$

Ans.
(3)

$K_{α} = (\frac{A - 4}{A}) Q$

${(K_{α})}_{A} = (\frac{196}{200}) Q and {(K_{α})}_{B} = (\frac{208}{212}) Q$

$\frac{{(K_{α})}_{A}}{{(K_{α})}_{B}} = \frac{196 \times 212}{200 \times 208} = \frac{2597}{2600}$

Want Us to Email you About Special Offers & Updates?

Solution

Q. 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 _______. [2026]

1 25482650

2 27062646

3 25972600

4 28622499

Ans. (3) Kα=(A-4A)Q (Kα)A=(196200)Q and (Kα)B=(208212)Q (Kα)A(Kα)B=196×212200×208=25972600