In which region lines of Balmer series like

Options

A. visible
B. infrered
C. ultra violet
D. radio wave

Answer

To determine in which region the lines of the Balmer series lie, we can follow these steps:

### Step 1: Understand the Balmer Series
The Balmer series corresponds to electronic transitions in hydrogen where the electron falls to the second energy level (n=2) from higher energy levels (n=3, 4, 5, ...).

### Step 2: Identify the Wavelengths
The wavelengths of the emitted light can be calculated using the Rydberg formula:
\[ \frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]
Where:
- \( R \) is the Rydberg constant (\( R = 1.097 \times 10^7 \, \text{m}^{-1} \))
- \( n_1 = 2 \) (for Balmer series)
- \( n_2 \) can be 3, 4, 5, etc.

### Step 3: Calculate Wavelengths for Different \( n_2 \) Values
1. **For \( n_2 = 3 \)**:
\[ \frac{1}{\lambda} = 1.097 \times 10^7 \left( \frac{1}{2^2} - \frac{1}{3^2} \right) = 1.097 \times 10^7 \left( \frac{1}{4} - \frac{1}{9} \right) \]
\[ = 1.097 \times 10^7 \left( \frac{9 - 4}{36} \right) = 1.097 \times 10^7 \times \frac{5}{36} \]
\[ \lambda \approx 6666.67 \, \text{Å} \]

2. **For \( n_2 = 4 \)**:
\[ \frac{1}{\lambda} = 1.097 \times 10^7 \left( \frac{1}{2^2} - \frac{1}{4^2} \right) = 1.097 \times 10^7 \left( \frac{1}{4} - \frac{1}{16} \right) \]
\[ = 1.097 \times 10^7 \left( \frac{4 - 1}{16} \right) = 1.097 \times 10^7 \times \frac{3}{16} \]
\[ \lambda \approx 4894 \, \text{Å} \]

3. **For \( n_2 = 5 \)**:
\[ \frac{1}{\lambda} = 1.097 \times 10^7 \left( \frac{1}{2^2} - \frac{1}{5^2} \right) = 1.097 \times 10^7 \left( \frac{1}{4} - \frac{1}{25} \right) \]
\[ = 1.097 \times 10^7 \left( \frac{25 - 4}{100} \right) = 1.097 \times 10^7 \times \frac{21}{100} \]
\[ \lambda \approx 4290 \, \text{Å} \]

### Step 4: Determine the Region of the Spectrum
The visible region of the electromagnetic spectrum is approximately from 4000 Å to 8000 Å. The calculated wavelengths for the Balmer series (6666.67 Å, 4894 Å, and 4290 Å) all fall within this range.

### Conclusion
The lines of the Balmer series lie in the **visible region** of the electromagnetic spectrum.

---