What is the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from the energy level with n = 4 to the energy level with n = 1 ? In which region of the electromagnetic spectrum does this radiation fall ?

Explanation

To find the wavelength of light emitted when an electron in a hydrogen atom transitions from the energy level with \( n = 4 \) to \( n = 1 \), we can use the Rydberg formula for hydrogen:

\[ \frac{1}{\lambda} = R \cdot Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]

where:
- \( R \) is the Rydberg constant, approximately \( 109678 \, \text{cm}^{-1} \)
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