Question

A hydrogen atom is in its fifth excited state. The atom emits a wavelength photon. Determine the maximum possible orbital angular momentum of the electron after emission. Express your answer as multiples of hbar

Answer 1

(√ 20) hbar.

Step-by-step explanation:

The first thing to do is to calculate the second principal quantum number, n from the formula for Calculating energy,E and this is done as given below;

Energy, E = 13.6 (1 / n^2 - 1/6).

(Where energy,E = 1240/ 7474).

Hence, when we solve the above equation for n, the principal quantum number = 5.

We know that the azimuthal quantum Number, l = (n- 1); 5 - 1 = 4.

Therefore, the maximum possible magnitude of the orbital angular momentum of the atom after emission = (√ 4 × 5) hbar.

the maximum possible magnitude of the orbital angular momentum of the atom after emission = (√ 20) hbar.

Note that hbar = 1.0545718 × 10-34 m2 kg / s.