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In which region lines of Balmer series l...

In which region lines of Balmer series like

A

visible

B

infrered

C

ultra violet

D

radio wave

Text Solution

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The correct Answer is:
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. ---
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