Determine the wavelength of light emitted when an electron in a hydrogen atom makes a transition from n = 5 to n = 3 energy levels.

• A. 656 nm
• B. 1282 nm
• C. 434 nm
• D. 486 nm

Answer: (C)

Verified step by step guidance

1. Understand that the problem involves an electron transition in a hydrogen atom, which can be analyzed using the Rydberg formula for hydrogen: $\frac{1}{\lambda }=R(\frac{1}{n^1}-\frac{1}{n^2})$, where $\lambda$ is the wavelength, $R$ is the Rydberg constant (approximately $1.097\times {10}^7 m-1$), and $n_1$ and $n_2$ are the principal quantum numbers of the initial and final energy levels.
2. Identify the initial and final energy levels: $n_1$ is 5 and $n_2$ is 3. Substitute these values into the Rydberg formula.
3. Calculate the difference in the inverse squares of the energy levels: $\frac{1}{3^2}-\frac{1}{5^2}$. This will give you the value needed to multiply by the Rydberg constant.
4. Multiply the result from the previous step by the Rydberg constant $R$ to find the inverse of the wavelength: $\frac{1}{\lambda }=R(\frac{1}{3^2}-\frac{1}{5^2})$.
5. Finally, take the reciprocal of the result to find the wavelength $\lambda$ in meters, and convert it to nanometers by multiplying by $10^9$.