Balmer series lies in which region of electromagnetic spectrum

Options

A. ultraviolet
B. infrared
C. visible range
D. microwave

Answer

To determine the region of the electromagnetic spectrum in which the Balmer series lies, we can follow these steps:

### Step 1: Understand the Balmer Series
The Balmer series is a set of spectral lines corresponding to transitions of electrons in a hydrogen atom from higher energy levels (n ≥ 3) to the second energy level (n = 2).

### Step 2: Identify the Wavelengths in the Balmer Series
The wavelengths of the Balmer series 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 (\( R \approx 1.097 \times 10^7 \, \text{m}^{-1} \))
- \( n_1 = 2 \) (for Balmer series)
- \( n_2 \) can take values 3, 4, 5, etc.

### Step 3: Calculate Minimum and Maximum Wavelengths
1. **Minimum Wavelength (n2 = ∞)**:
\[ \frac{1}{\lambda} = R \left( \frac{1}{2^2} - 0 \right) = \frac{R}{4} \]
\[ \lambda = \frac{4}{R} \approx \frac{4}{1.097 \times 10^7} \approx 364 \, \text{nm} \]

2. **Maximum Wavelength (n2 = 3)**:
\[ \frac{1}{\lambda} = R \left( \frac{1}{2^2} - \frac{1}{3^2} \right) = R \left( \frac{1}{4} - \frac{1}{9} \right) = R \left( \frac{5}{36} \right) \]
\[ \lambda = \frac{36}{5R} \approx \frac{36}{5 \times 1.097 \times 10^7} \approx 657 \, \text{nm} \]

### Step 4: Determine the Region of the Electromagnetic Spectrum
The calculated wavelengths for the Balmer series range from approximately 364 nm to 657 nm. The visible region of the electromagnetic spectrum is approximately from 400 nm to 700 nm.

### Conclusion
Since the wavelengths of the Balmer series fall within the visible range (400 nm to 700 nm), we conclude that the Balmer series lies in the visible region of the electromagnetic spectrum.

### Final Answer
The Balmer series lies in the visible region of the electromagnetic spectrum.

---