Question

The ratio of series limit frequencies of balmer series to that of bracket series for a hatom is

Answer 1

I don't know

I don't know

I don't know

I don't know

Answer 2

For Balmer series (n1 =2)

By Rydberg’s law-

$\frac{1}{λ} = R_{H} [ \frac{1}{{N_1}^{2} }- \frac{1}{{N_2}^{2}}]$

where λ= wavelength=> $v = c. R_{4} [ \frac{1}{{N_1}^{2} }- \frac{1}{{N_2}^{2}}]$

where C = speed of light, v = frequency.

$v_m = c. R_{H} [ \frac{1}{4} - \frac{1}{ \infty }] = \frac{R_H . c}{4}$

For Bracket series (n1 =4)

$v_m = c. R_{H} [ \frac{1}{16} - \frac{1}{ \infty }] = \frac{R_4 . c}{16}$

$Ratio \times \frac{∂_m (Balmer)}{D_m (Boacket)} = \frac{16}{4} = \frac{4}{1}$

Ratio = 4:1 (ans.)