Quantum Mechanics - Spectroscopic Notation

A 3p electron is found in the ³P_3/2 energy level of a hydrogen atom. Which of the following is true about the electron in this state?

A. It is allowed to make an electric dipole transition to the ²S_1/2 level
B. It is allowed to make an electric dipole transition to the ²P_1/2 level
C. It has quantum numbers l = 3, j = 3/2, s = 1/2
D. It has quantum numbers n = 3, j = l, s = 3/2
E. It has exactly the same energy as it would in the ³D_3/2 level

(GR9677 #41)

Solution:

Spectroscopic notation: N^2s+1 L_j=l+s

For ³P_3/2  : 

P → l = 1
j = 3/2

→ (C) and (D) are FALSE

Selection rules (for electron transition):

1.	Principal quantum number	:	∆n = anything
2.	Orbital angular momentum	:	∆l = ±1
3.	Magnetic quantum number	:	∆ml = 0, ±1
4.	Spin	:	∆s = 0
5.	Total angular momentum	:	∆j = 0, ±1, but j = 0 ↛j = 0

(A) TRUE
Transition for ∆l = 0 is allowed.

(B) FALSE
Transition for ∆l = 0 is not allowed.

(E) FALSE
Electron can not move to different energy level (P to D) while maintaining the same energy.

Answer: A

Classical Mechanics - Rotational Motion

Questions 41-42

A cylinder with moment inertia 4 kgm² about a fixed axis initially rotates at 80 radians per second about this axis. A constant torque is applied to slow it down to 40 radians per second. The kinetic energy lost by the cylinder is

A. 80 J
B. 800 J
C. 4000 J
D. 9600 J
E. 19,200 J

(GR9277 #41) 

Solution:

Rotational Kinetic Energy:  



Answer: D

Nuclear & Particle Physics - Binding Energy

Which of the following nuclei has the largest binding energy per nucleon? (Consider the most abundant isotope of each element.) 

A. Helium
B. Carbon
C. Iron
D. Uranium
E. Plutonium

(GR8677 #41)

Solution:

Uranium and Plutonium: decay spontaneously → very low binding energy.
Iron: the most stable element → tightly bound → the largest binding energy.

Source: hyperphysics.phy-astr.gsu.edu

Answer: C

Electromagnetism - Maxwell Equation

Maxwell’s equations can be written in the form shown below. If magnetic charge exists and if it is conserved, which of these equations will have to be changed

A. I only

B. II only

C. III only

D. I and IV

E. II and III

(GR0177 #41)

Solution:

Gauss Law for magnetism:

• It implies there is no magnetic monopoles.
• If there is magnetic monopole:

Faraday Law of Induction:

• The electric field is equal to the negative of the rate of change of the magnetic flux.
• If there is magnetic monopole, an extra term (involving the current of magnetic monopoles) must be added to the right-hand side of the equation in order to make it self-consistent.

Answer: E