Using Bohr's postulates, derive the expression for the frequency of radiation emitted when electron in hydrogen atom undergoes transition from higher energy state (quantum number `n_(i)`) to the lower state, (`n_(f))`. When electron in hydrogen atom jumps from energy state `n_(i) = 4` to `n_(f) = 3, 2, 1`, identify the spectral series to which the emission lines belong.

Explanation

To derive the expression for the frequency of radiation emitted when an electron in a hydrogen atom transitions from a higher energy state (quantum number \( n_i \)) to a lower energy state (\( n_f \)), we can follow these steps:

### Step 1: Understand Bohr's Model
According to Bohr's model, electrons revolve around the nucleus in specific stable orbits without radiating energy. The energy levels of these orbits are quantized and given by the formula:

\[ E_n = -\frac{m e^4}{8 \epsilon_0^2 h^2 n^2} \]
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