Question

what is the wavelength in nm of the light emitted by an electron going from n = 5 level to n = 2 level in a hydrogen atom? (use the book for constants.) a) 1920 b) 363 c) 2280 d) 432 e) 95

Answer 1

The wavelength in nm of light emitted by an electron transitioning from n = 5 to n = 2 in a hydrogen atom is calculated using the Rydberg formula, converting the result to nanometers.

Step-by-step explanation:

To determine the wavelength in nm of the light emitted by an electron transitioning from n = 5 to n = 2 in a hydrogen atom, we can use the Rydberg formula:

1/λ = R * (1/n² - 1/n²), where λ is the wavelength, R is the Rydberg constant (1.097 x 10^7 m^-1), n is the principal quantum number, and the values are squared.

So we calculate as follows:

1. Identify the initial and final energy levels (n initial = 5, n final = 2).
2. Apply the Rydberg formula: 1/λ = R * (1/2^2 - 1/5^2)
3. Simplify and calculate the result, then convert the wavelength from meters to nanometers (1 nm = 10^-9 m).

Thus, the wavelength of the emitted light (rounded to the nearest integer) matches one of the given options in the question.