Question

A Hydrogen atom initially in n = 3 , l = 2 , m_l = -1, and m_s =+1/2 state absorbs a photon and transitioned to n = 4 state.

Question: What are the possible final quantum numbers?

	A.	n = 4,  l =  2,  ml  = -1, ms   = +1/2
	B.	n = 4, l = 2, ml = -1, ms = +1/2
	C.	n = 4 , l = 1 , ml  = 0, ms = +1/2
	D.	n = 4, l = 3 , ml  = -1, ms  = +1/2
	E.	n = 4, l = 1, ml = -1, ms = +1/2

Answer 1

Selection rules are :

L = +1 or -1,

m_l = 0, +1 or -1,

m_s = 0.

Hence, L = 2 + 1 or 2 - 1 = 3 or 1.

Also, m_l = -1 or -2 or 0,

And, m_s = + 1 / 2.

Now, since the electron is absorbing a photon, hence it is jumping to a higher energy state.

Also, we know, L = 3 state is energtically higher than L = 1 state.

Hence, correct option is : (D) n = 4, L = 3, m_l = - 1, m_s = + 1 / 2.