what is the frequency of light emitted when the electron in a hydrogen atom undergoes a transition from energy level n

Complete question is;

What is the frequency of light emitted when the electron in a hydrogen atom undergoes a transition from energy level n=6 to level n=3?

Frequency = 2.742 × 10^(14) s^(-1)

Explanation:

First of all, the energy of hydrogen electron from online values is;

E_n = -2.18 × 10^(-18) × (1/n²) J

n is the principal quantum number

We are told that hydrogen atom undergoes a transition from energy levels n = 3 to n = 6.

Thus, it means we have to find the difference between the electrons energy in the energy levels n = 3 to n = 6.

Thus;

E_n = E_6 - E_3

Thus;

E_n = [-2.18 × 10^(-18) × (1/6²)] - [-2.18 × 10^(-18) × (1/3²)]

E_n = (2.18 × 10^(-18)) × [-1/36 + 1/9]

E_n = 0.1817 × 10^(-18) J

From Planck expression, we can find the frequency. Thus;

E = hf

Where h is Planck's constant = 6.626 × 10^(-34) m²kg/s

Thus;

0.1817 × 10^(-18) = 6.626 × 10^(-34) × f

f = (0.1817 × 10^(-18))/(6.626 × 10^(-34))

f = 2.742 × 10^(14) s^(-1)