For an atom of hydrogen without the effects of an external ...

[jessicacav]

For an atom of hydrogen without the effects of an external magnetic field, an electron transition from the 3P subshell to the 2P subshell is called a forbidden transition. Why is this so?
  a. Electrons in hydrogen are forbidden from transitioning in that way due to peculiarities unique to solutions of Schrdinger's equation for hydrogen.
  b.The normal Zeeman effect prohibits certain transitions from occurring.
  c. Since the electron at low energies must pass through the nucleus, nuclear effects prevent certain transitions to orbits through the nucleus.
  d.An atom that changes energy through transitioning must either absorb or emit a photon.

Question 2

Which of the following states of the hydrogen atom, as defined only by the principal quantum number, angular momentum quantum number, and magnetic quantum number, is allowed?
 

a. n = 0, l = 2, m_l = 1
  b. n = 5, l = 2, m_l = 3
  c. n = 0, l = 1, m_l = 2
  d. n = 5, l = 2, m_l = 0
  e. n = 2, l = 2, m_l = 0

Question 3

For an atom of hydrogen where the quantum number n = 3, how many possible independent configurations of the atom exist (consider principal quantum number n, angular momentum quantum number l, magnetic quantum number m_l, and magnetic spin quantum number m_s)?
 

a. 18
  b. 8
  c. 32
  d. 26
  e. infinite

[Smiles0805]

Answer to Question 1

d.
A photon must be emitted when the electron transitions from n = 3 to n = 2, and the photon carries a specific angular momentum of l = 1. The transition from a P subshell to another Psubshell, both with angular momentum l = 2, is therefore forbidden.

Answer to Question 2

d.
The rules governing the configurations of the hydrogen atom are n > 0, l < n, and l m_l. When n = 5, l must be 4 or less and when l = 2, m_l must be 2 or less. The restrictions set by the solution to Schrdinger's equation are satisfie

Answer to Question 3

a.
For n = 3, l = 2, 1, 0; for each l, m_l, = -l, -(l - 1), ..., (l - 1), l; and for each of the states given by n, l, and m_l, m_s = -1/2, 1/2. This corresponds to 18 individual states.