Question

The electron in a hydrogen atom makes transition from M shell to L. The ratio of magnitudes of initial to final centripetal acceleration of the electron is

• A. $9:4$
• B. $81:16$
• C. $4:9$
• D. $16:81$

Answer 1

The correct option is D $16:81$

Since,
$r_n\propto n^2$
$v_n\propto \frac{1}{n}$
$a_n\propto \frac{v_n^2}{r_n}$
$a_n\propto \frac{1}{n^2\times n^2}$
$a_n\propto \frac{1}{n^4}$
$a_n=\frac{k}{n^4}$
For M to L the n value will vary from 3 to 2
$a_3=\frac{k}{81}$
$a_2=\frac{k}{16}$
$\frac{a_M}{a_L}=\frac{a_3}{a_2}=\frac{16}{81}$