The largest wavelength in the ultraviolet reg | vedclass

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

Question

(B) The Rydberg formula for the hydrogen atom $(Z=1)$ is given by $\frac{1}{\lambda} = R \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right)$.The ultravi

Vedclass · Accepted Answer

$823$

Vedclass · Answer

(B) The Rydberg formula for the hydrogen atom $(Z=1)$ is given by $\frac{1}{\lambda} = R \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} ight)$.The ultraviolet region corresponds to the Lyman series $(n_f = 1)$. The largest wavelength corresponds to the minimum energy transition,which is from $n_i = 2$ to $n_f = 1$.Given $\lambda_{max, UV} = 122 \ nm$,we have $\frac{1}{122} = R \left( \frac{1}{1^2} - \frac{1}{2^2} ight) = R \left( 1 - \frac{1}{4} ight) = \frac{3R}{4}$.Thus,$\frac{1}{R} = 122 	imes \frac{3}{4} = 91.5 \ nm$.The infrared region includes the Paschen series $(n_f = 3)$,Brackett series $(n_f = 4)$,and Pfund series $(n_f = 5)$. The smallest wavelength in the entire infrared region corresponds to the maximum energy transition,which is the limit of the Paschen series ($n_f = 3$ to $n_i = \infty$).$\frac{1}{\lambda_{min, IR}} = R \left( \frac{1}{3^2} - \frac{1}{\infty^2} ight) = \frac{R}{9}$.$\lambda_{min, IR} = \frac{9}{R} = 9 	imes 91.5 = 823.5 \ nm$.Rounding to the nearest integer,we get $823 \ nm$. Therefore,option $(B)$ is correct.

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 $nm$)

Similar Questions

Let $\lambda_P$ and $\lambda_L$ be the longest wavelengths observed in the Paschen and Lyman series respectively. Choose the correct option.

In which of the following series does the $121.5 \ nm$ line of the spectrum of the hydrogen atom lie?

Assertion: In the Lyman series,the ratio of minimum and maximum wavelength is $\frac{3}{4}$.
Reason: The Lyman series constitutes spectral lines corresponding to transitions from higher energy levels to the ground state of the hydrogen atom.

When an electron in a hydrogen atom jumps to the innermost orbit,the radiation emitted belongs to which one of the following series?

If the wavelength of the first member of the Lyman series of hydrogen is $\lambda$,what is the wavelength of the second member?

Vedclass Test Series

Exam Paper Generator

Online Exam Module