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What would be the wavelength of a photon emitted when the electron in a hydrogen atom moves from the \( n = 5 \) to \( n = 3 \) state?

Options:
A. 121.6 nm
B. 102.6 nm
C. 97.3 nm
D. 93.7 nm

Answer :

Final answer:

The wavelength of a photon emitted during a transition from n = 5 to n = 3 in a hydrogen atom is 102.6 nm, So the correct answer is option b.102.6 nm

Explanation:

The wavelength of a photon emitted when an electron in a hydrogen atom transitions from the n = 5 to the n = 3 state can be determined using the Rydberg formula, which relates the wavelength (λ) of the emitted photon to the initial (n1) and final (n2) energy levels:

Rydberg formula: \(\frac{1}{\lambda} = R\left(\frac{1}{n_{2}^2} - \frac{1}{n_{1}^2}\right)\), where R is the Rydberg constant (1.097 x 107 m-1).

Plugging in the values for the given transition (n1 = 5, n2 = 3), we will find the wavelength that corresponds to this transition. The correct answer based on the given options and on the Rydberg formula calculation would be 102.6 nm, which is option b. This transition falls within the ultraviolet range of the electromagnetic spectrum.

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