The ratio of the longest to shortest waveleng | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For the Brackett series,the wavelength $\lambda$ is given by the Rydberg formula: $\frac{1}{\lambda} = R \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2}

Vedclass · Accepted Answer

$\frac{25}{9}$

Vedclass · Answer

(A) For the Brackett series,the wavelength $\lambda$ is given by the Rydberg formula: $\frac{1}{\lambda} = R \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2} ight]$,where $n_1 = 4$ and $n_2 = 5, 6, 7, \dots$ The longest wavelength $(\lambda_{\max})$ corresponds to the transition from $n_2 = 5$ to $n_1 = 4$: $\frac{1}{\lambda_{\max}} = R \left[ \frac{1}{4^2} - \frac{1}{5^2} ight] = R \left[ \frac{1}{16} - \frac{1}{25} ight] = R \left[ \frac{25 - 16}{400} ight] = \frac{9R}{400}$ $\lambda_{\max} = \frac{400}{9R}$ The shortest wavelength $(\lambda_{\min})$ corresponds to the transition from $n_2 = \infty$ to $n_1 = 4$: $\frac{1}{\lambda_{\min}} = R \left[ \frac{1}{4^2} - \frac{1}{\infty^2} ight] = R \left[ \frac{1}{16} - 0 ight] = \frac{R}{16}$ $\lambda_{\min} = \frac{16}{R}$ The ratio of the longest to shortest wavelength is: $\frac{\lambda_{\max}}{\lambda_{\min}} = \frac{400/9R}{16/R} = \frac{400}{9 	imes 16} = \frac{25}{9}$

The ratio of the longest to shortest wavelengths in the Brackett series of hydrogen spectra is

Similar Questions

In the hydrogen spectrum,the wavelengths of light emitted in a series of spectral lines is given by the equation,$\frac{1}{\lambda}=R\left(\frac{1}{4^{2}}-\frac{1}{n^{2}}\right)$,where $n=5, 6, 7, \ldots$ and $R$ is Rydberg's constant. Identify the series and wavelength region.

An electron changes its position from orbit $n = 4$ to the orbit $n = 2$ of an atom. The wavelength of the emitted radiation is ($R =$ Rydberg's constant).

If Rydberg's constant is $R$,the longest wavelength of radiation in Paschen series will be $\frac{\alpha}{7 R}$,where $\alpha=$ . . . . . .

Which line has the maximum wavelength and frequency in each series of the hydrogen spectrum?

The ratio of the wavelength of the last line of the Paschen series to that of the Balmer series is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module