According to the Bohr model, what is the wavelength of light emitted when an electron transitions from the n=2 to the n=1 energy level in a hydrogen atom?

• A. 656.3 nm
• B. 121.6 nm
• C. 434.0 nm
• D. 486.1 nm

Answer: (B)

Verified step by step guidance

1. Identify the initial and final energy levels for the electron transition: n=2 (initial) and n=1 (final).
2. Use the Rydberg formula to calculate the wavelength of light emitted during the transition: \( \frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \), where \( R_H \) is the Rydberg constant (1.097 x 10^7 m^-1), \( n_1 \) is the final energy level, and \( n_2 \) is the initial energy level.
3. Substitute the values for \( n_1 = 1 \) and \( n_2 = 2 \) into the Rydberg formula: \( \frac{1}{\lambda} = 1.097 \times 10^7 \left( \frac{1}{1^2} - \frac{1}{2^2} \right) \).
4. Calculate the difference in the terms inside the parentheses: \( \frac{1}{1^2} - \frac{1}{2^2} = 1 - \frac{1}{4} = \frac{3}{4} \).
5. Solve for \( \lambda \) by taking the reciprocal of the product: \( \lambda = \frac{1}{1.097 \times 10^7 \times \frac{3}{4}} \).