Nuclear & Particle Physics - Muon

Except for mass, the properties of the muon most closely resemble the properties of the

A. electron
B. graviton
C. photon
D. pion
E. proton

(GR8677 #16)

Solution:

(A) TRUE
Muon and electron are elementary particles → fermions (half-integer spin) → leptons (one unit charge)

(B) FALSE
Graviton is gravity force carrier → boson (integer spin)

(C) FALSE
Photon is EM force carrier → boson (integer spin)

(D) FALSE
Pion is composite particle → meson (consist of quark-antiquark)

(E) FALSE
Proton is composite particle → baryon (consist of 3 quarks)

click image to enlarge

Answer: A

Nuclear & Particle Physics - Photoelectric

Questions 31-33 refer to the apparatus used to study the photoelectric effect (see GR8677 #31).

The photoelectric equation is derived under the assumption that

1. Electrons are restricted to orbits of angular momentum nħ, where n is an integer
2. Electrons are associated with waves of wavelength λ = h/p, where p is momentum
3. Light is emitted only when electrons jump between orbits
4. Light is absorbed in quanta of energy E = hv
5. Light behaves like a wave

(GR8677 #32)

Solution:

According to the classical Maxwell wave theory of light, the average energy carried by an emitted electron should increase with the intensity of the incident light.

However, in photoelectric case, the energies of the emitted electrons are independent of the intensity of the incident radiation.

Einstein resolved this paradox by proposed that the incident light consisted of individual quanta, called photons, that interacted with the electrons in the metal like discrete particles, rather than as continuous waves.

Answer: D

Nuclear & Particle Physics - Selection Rules

A transition in which one photon is radiated by the electron in a hydrogen atom when the electron's wave function changes from ψ₁ to ψ₂ is forbidden if ψ₁ and ψ₂

A. have opposite parity
B. are orthogonal to each other
C. are zero at the center of the atomic nucleus
D. are both spherically symmetrical
E. are associated with different angular momenta

(GR8677 #48)

Solution:

Selection rules:

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. FALSE
It’s not related to the selection rules.

B. FALSE
In any transition, eigenstates should always be mutually orthogonal.

C. FALSE.
Eigenstates zero at the center → l 0 could change, for example from 3 to 2. This is allowed.

D. TRUE.
If both initial and final states have spherically symmetrical wave functions, then they have the same angular momentum. l = 0 → l = 0 is forbidden.

E. FALSE.
The selection rules require l to change.

Answer: D