Question

What is the value of ni for an electron that emits a photon of wavelength 93.85 nm when it returns to the ground state in the H atom?

Answer 1

It is given that electrons emits a photon of wavelength 93.85 nm and then returns to ground state from ni the energy state, $\lambda = 93.85 \times 10^-7 cm$

now using Rydberg formula for wavelength of photon ejected

we know that

$\frac{1}{\lambda}$ =$R_h(\frac{1}{n_f^2} -\frac{1}{n_i^2})$

here, $\lambda$ = wavelength of photon ejected, $n_i =$ energy level from which electron coming and $n_f$ = energy level at which it is going=1

$R_h$ = Rydberg constant = 109737.32 cm-1

now ,

$\frac{1}{\lambda} = 109737.32 ( \frac{1}{1^2} - \frac{1}{n_i^2} )$

$\frac{1}{93.85 \times10^-7} = 109737.32 (1- \frac{1}{n_i^2})$

.010655 $\times 10^7 =109737.32 (1-\frac{1}{n_i^2})$

$\frac{1.06 \times10^5}{109737.32 } =(1- \frac{1}{n_i^2})$

.97098= 1 $-\frac{1}{n_i^2}$

$\frac{1}{n_i^2} = 1-.97098$

$n_i^2 = \frac{1}{.029}$

$n_i^2= 34.46$

$n_i$ =5.87

so here we take minimum energy level as $n_i$ =6