What are the postulates of Bohr's model of hydrogen atom ? Discuss the importance of this model to explain various series of line spectra in hydrogen atom.

Answer

### Step-by-Step Solution

**Step 1: Introduction to Bohr's Model**
Bohr's model of the hydrogen atom was proposed by Niels Bohr in 1913. It was a significant advancement in understanding atomic structure, particularly for hydrogen, the simplest atom.

**Step 2: Postulates of Bohr's Model**
1. **Electrons in Circular Orbits**: Electrons revolve around the nucleus in specific, fixed circular orbits. These orbits are known as "stationary states."

2. **Quantized Energy Levels**: Each orbit corresponds to a specific energy level. The energy of the electron is quantized, meaning it can only occupy certain energy levels.

3. **Energy and Orbit Size**: As the principal quantum number (n) increases, the size and energy of the orbits also increase. Higher n values correspond to larger orbits and higher energy states.

4. **No Energy Emission in Orbits**: While in these stationary orbits, electrons do not emit or absorb energy. They can only change energy levels by jumping between orbits.

5. **Quantization of Angular Momentum**: The angular momentum of the electron in its orbit is quantized and is given by the formula:
\[ L = n \frac{h}{2\pi} \]
where \( L \) is the angular momentum, \( n \) is the principal quantum number, and \( h \) is Planck's constant.

**Step 3: Importance of Bohr's Model in Explaining Line Spectra**
Bohr's model is crucial for explaining the line spectra of hydrogen. When an electron transitions between energy levels:
- **Absorption of Energy**: When an electron moves from a lower orbit to a higher orbit, it absorbs energy (e.g., from a photon).
- **Emission of Energy**: When it falls back to a lower orbit, it emits energy in the form of light. The emitted light corresponds to specific wavelengths, creating a line spectrum.

The different series of spectral lines (Lyman, Balmer, Paschen, Brackett) arise from transitions between specific energy levels:
- **Lyman Series**: Transitions to n=1 (ultraviolet region).
- **Balmer Series**: Transitions to n=2 (visible region).
- **Paschen Series**: Transitions to n=3 (infrared region).
- **Brackett Series**: Transitions to n=4 (infrared region).

These series demonstrate how the quantized energy levels lead to distinct spectral lines.