Calculate the wavelength of the light emitted when an electron in a hydrogen atom makes the transition from n=2 to n=1 using the Bohr model.

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

Answer: (C)

Verified step by step guidance

1. Identify the initial and final energy levels of the electron transition. In this case, the electron transitions from n=2 to n=1.
2. Use the Rydberg formula to calculate the energy difference between these levels: $E_n=\frac{-R_H}{n^2}$, where $R_H$ is the Rydberg constant for hydrogen.
3. Calculate the energy difference using the formula: $\mathrm{\Delta E}=E_1-E_2$. Substitute the values for n=1 and n=2 into the Rydberg formula to find $\mathrm{\Delta E}$.
4. Convert the energy difference to wavelength using the equation: $\lambda =\frac{\mathrm{hc}}{\mathrm{\Delta E}}$, where $h$ is Planck's constant and $c$ is the speed of light.
5. Substitute the values for Planck's constant and the speed of light into the equation to find the wavelength of the emitted light.