Question

When the electron in a hydrogen atom moves from n = 5 to n = 2, light with a wavelength of ________ nm is emitted?

Answer 1

The wavelength of light emitted when an electron in a hydrogen atom transitions from n = 5 to n = 2 is 434 nm, which falls within the blue spectrum.

Step-by-step explanation:

When the electron in a hydrogen atom moves from n = 5 to n = 2, light with a specific wavelength is emitted. This transition falls under the Balmer series, which includes the transitions of electrons from higher energy levels to n = 2. The specific wavelengths of the Balmer series for n = 3 to n = 2 is 656 nm (red), for n = 4 to n = 2 is 486 nm (green), for n = 5 to n = 2 is 434 nm (blue), and for n = 6 to n = 2 is 410 nm (violet). Therefore, the wavelength of light emitted when an electron transitions from n = 5 to n = 2 is 434 nm.

Answer 2

In order for an electron to move to a higher energy level, the photon is absorbed by
the atom. The energy of the photon must be at least enough to raise the electron
from energy level 2 to level 5. The wavelength w can be found by Rydberg's formula
1/w = R(1/L² - 1/U²), where L and U are the lower and upper energy levels, in this
case 2 and 5. R is the Rydberg constant, experimentally found to be10,967,758
waves per meter for hydrogen. So the wavelength w is: 1/w = R(1/4 - 1/25) = 0.21R
The value we get is w = 4.34 * 10**-7 meter, or 434 nanometers and it is absorbed
by the atom to cause the electron to move to the higher energy level.
Answer choice A above is the best choice. Hope this answers your question.