Physics Problems & Solutions: Gamma Decay

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Nuclear & Particle Physics - Positronium

Positronium is the bound state of an electron and a positron. Consider only the states of zero orbital angular momentum l = 0. The most probable decay product of any such state of positronium with spin zero (singlet is)

A. 0 photons
B. 1 photons
C. 2 photons
D. 3 photons
E. 4 photons

(GR9677 #53)

Solution:

The singlet state, s = 0 of Positronium is known as para-Positronium, decays preferentially into two gamma rays.

It can decay into any even number of photons (2, 4, 6, ...), but the probability quickly decreases with the number.

Thus, the most probable decay product of singlet state of positronium is 2 photons.

Answer: C

Nuclear & Particle Physics - Radioactivity

Suppose that

decays by natural radioactivity in two stages to $_{Z-1}^{A-4}Y$ . The two stages would most likely be which of the following?

	First Stage	Second Stage
A.	β⁻ emission with an antineutrino	α emission
B.	β⁻ emission	α emission with a neutrino
C.	β⁻ emission	γ emission
D.	Emission of a deuteron	Emission of two neutrons
E.	α emission	γ emission

(GR9677 #30)

Solution:

→ First Stage → Second Stage → $_{Z-1}^{A-4}Y$

by natural decay.

A. TRUE.
β⁻ decay: emission of an electron and electron anti-neutrino,

$_Z^AX \rightarrow {_{Z+1}^A}X'+{_{-1}^0}\beta+\bar{\nu}$

α decay: emission of a Helium nucleus resulting in the loss of two protons and two neutrons,

$_Z^AX \rightarrow {_{Z-2}^{A-4}}X'+{_{2}^4}He$

Therefore,

$\\_Z^AX \rightarrow \beta^-$ decay$\rightarrow \alpha $ decay$\rightarrow {_{Z-1}^{A-4}}Y\\\\_Z^AX \rightarrow {_{Z+1}^A}X'\rightarrow {_{Z+1-2}^{A-4}}X''\rightarrow {_{Z-1}^{A-4}}Y$

B. FALSE.
β⁻ decay always emits an anti-neutrino
α decay does not emit neutrino

C. FALSE.
γ decay: photon emission with no change in mass number A or atomic number Z

$_Z^AX \rightarrow{ _Z^AX}'+\gamma$

Therefore,

$_Z^AX \rightarrow {_{Z+1}^A}X'\rightarrow {_{Z+1}^A}X''\rightarrow {_{Z+1}^A}Y$

D. FALSE.
Deuteron decay:
Deuteron (nucleus of deuterium) is a stable particle.
Deuteron decay is rare, not natural.

E. FALSE.

$_Z^AX \rightarrow {_{Z-2}^{A-4}}X'\rightarrow {_{Z-2}^{A-4}}X''\rightarrow {_{Z-2}^{A-4}}Y$

Answer: A

Nuclear & Particle Physics – Conservation Laws

Which of the following reasons explains why a photon cannot decay to an electron and a positron γ → e⁻+ e⁺in free space?

A. Linear momentum and energy are not both conserved
B. Linear momentum and angular momentum are not both conserved
C. Angular momentum and parity are not both conserved
D. Parity and strangeness are not both conserved
E. Charge and lepton number are not both conserved

(GR9677 #96)

Solution:

See GR0177 #99

Answer: A