Question

Line spectra from all regions of the electromagnetic spectrum, including the Paschen series of infrared lines for hydrogen, are used by astronomers to identify elements present in the atmospheres of stars. Calculate the wavelength of the photon emitted when the hydrogen atom undergoes a transition from n = 5 to n = 3. (R = 2.179 x 10-18 J R = 1.096776 x 10^7 m-1) A. 205.1 nm B. 384.6 nm C. 683.8 nm D. 1282 nm E. > 1500 nm

Answer 1

Answer:

The correct answer is option D.

Explanation:

Using Rydberg's Equation for hydrogen atom:

$\bar{\nu}=\frac{1}{\lambda}=R_H\left(\frac{1}{n_i^2}-\frac{1}{n_f^2} \right )$

Where,

$\bar{\nu}$ = Wave number

$\lambda$ = Wavelength of radiation

$R_H$ = Rydberg's Constant

$n_f$ = Higher energy level

$n_i$= Lower energy level

We have:

$n_f=5, n_i=3$

$R_H=1.096776\times 10^7 m^{-1}$

$\frac{1}{\lambda}=1.096776\times 10^7 m^{-1}\times \left(\frac{1}{3^2}-\frac{1}{5^2} \right )$

$\frac{1}{\lambda}=1.096776\times 10^7 m^{-1}\times \frac{16}{225}$

$\lambda =1.2822\times 10^{-6} m=1282.2 nm\approx 1282 nm$

($1 m= 10^9 nm$)

The wavelength of the photon emitted when the hydrogen atom undergoes a transition from n = 5 to n = 3 is 1282 nm.