Question

If 917 Å be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be _____ Å.

Answer 1

Correct Answer: 3668

For the Lyman series, the lowest wavelength corresponds to the transition from \( n = \infty \) to \( n = 1 \), and the wavelength is given as 917 Å.
For the Balmer series, the lowest wavelength corresponds to the transition from \( n = \infty \) to \( n = 2 \).
The energy \( E_0 \) for the Lyman series is related to the wavelength \( \lambda_0 \) by: \[ E_0 = \frac{hc}{\lambda_0} \] For Lyman, \( \lambda_0 = 917 \, \text{Å} \), so: \[ E_0 = \frac{hc}{917 \, \text{Å}} \] For the Balmer series, the energy is related by: \[ \frac{E_0}{4} = \frac{hc}{\lambda} \] where \( \lambda \) is the wavelength of the Balmer series. Substituting the energy of the Lyman series: \[ \frac{hc}{4 \times 917 \, \text{Å}} = \frac{hc}{\lambda} \] Thus, the wavelength for the Balmer series is: \[ \lambda = 917 \times 4 = 3668 \, \text{Å} \] Therefore, the lowest wavelength of the Balmer series is 3668 Å.