Physics Problems & Solutions: Beta Decay

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Nuclear & Particle Physics - Beta Decay

When the beta decay of ⁶⁰Co nuclei is observed at low temperature in a magnetic field that aligns spins of the nuclei, it is found that the electrons are emitted preferentially in a direction opposite to the ⁶⁰Co spin direction. Which of the following invariances is violated by this decay

A. Gauge invariance
B. Time invariance
C. Translation invariance
D. Reflection invariance
E. Rotation invariance

(GR9677 #34)

Solution:

Wu experiment, 1957: beta decay of Cobalt-60 shows that electrons are emitted preferentially in a direction opposite to the ⁶⁰Co spin direction → Parity violation by the weak interaction.

A. Gauge invariance → related to conservation of charge
B. Time invariance → energy
C. Translation invariance → momentum
D. Reflection invariance → parity
E. Rotation invariance → angular momentum

Answer: D

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 - Radioactive

A sample of radioactive nuclei of a certain element can decay only by $\gamma$ -emission and $\beta$ -emission. If the half-life for $\gamma$ -emission is 24 minutes and that for $\beta$ -emission is 36 minutes, the half-life for sample is

A. 30 minutes
B. 24 minutes
C. 20.8 minutes
D. 14.4 minutes
E. 6 minutes

(GR0177 #66)

Solution:

Total half-time for 2 or more processes:

$\frac{1}{T}=\frac{1}{t_1} +\frac{1}{t_2} +...$

For the sample with $\gamma$ and $\beta$ emissions:

$\\\frac{1}{T}=\frac{1}{24}+\frac{1}{36}=\frac{36+24}{24\times 36}=\frac{60}{864}\rightarrow T=14.4$

Answer: D