What is the shortest wavelength present in th | vedclass

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

Question

(D) For the Paschen series,the Rydberg formula is given by $\frac{1}{\lambda} = R \left[ \frac{1}{3^2} - \frac{1}{n^2} \right]$,where $n = 4, 5, 6, \d

Vedclass · Accepted Answer

$820$

Vedclass · Answer

(D) For the Paschen series,the Rydberg formula is given by $\frac{1}{\lambda} = R \left[ \frac{1}{3^2} - \frac{1}{n^2} ight]$,where $n = 4, 5, 6, \dots$ To find the shortest wavelength,we consider the limit where $n = \infty$. Substituting $n = \infty$ into the formula: $\frac{1}{\lambda_{\min}} = R \left[ \frac{1}{9} - 0 ight] = \frac{R}{9}$. Thus,$\lambda_{\min} = \frac{9}{R}$. Given the Rydberg constant $R \approx 1.097 	imes 10^7 \ m^{-1}$: $\lambda_{\min} = \frac{9}{1.097 	imes 10^7} \approx 8.204 	imes 10^{-7} \ m$. Converting to nanometers: $\lambda_{\min} \approx 820.4 \ nm \approx 820 \ nm$.

What is the shortest wavelength present in the Paschen series of spectral lines (in $nm$)?

Similar Questions

Given the value of Rydberg constant is $10^7 \, m^{-1}$,the wave number of the last line of the Balmer series in the hydrogen spectrum will be:

Which one of the series of hydrogen spectrum is in the visible region?

The largest wavelength in the ultraviolet region of the hydrogen spectrum is $122 \ nm$. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is (in $nm$)

The wavelength of the yellow line of sodium is $5896 \mathring{A}$. Its wave number will be:

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).

Vedclass Test Series

Exam Paper Generator

Online Exam Module