Question

The wavelength of a spectral line in the second order of the hydrogen spectrum is 2.82 Å. The wavelength of the spectral line in the first order is:

• A. 5.64 Å
• B. 8.64 Å
• C. 10.82 Å
• D. 4.82 Å

Hint:

To find the wavelength in the first order, simply multiply the wavelength in the second order by 2.

Answer 1

The Correct Option is A

Step 1: Use the relation between wavelengths in different orders. For the hydrogen spectrum, the wavelength in the \( m \)-th order is related to the wavelength in the first order by: \[ \lambda_m = \frac{\lambda_1}{m} \] Where \( \lambda_1 \) is the wavelength in the first order and \( m \) is the order of the spectrum.
Step 2: Solve for \( \lambda_1 \). Given \( \lambda_2 = 2.82 \, \text{Å} \) for the second order, we have: \[ \lambda_1 = 2 \times \lambda_2 = 2 \times 2.82 \, \text{Å} = 5.64 \, \text{Å} \]