Physics Problems & Solutions: Deuteron

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Nuclear & Particle Physics - Standard Model

According to the Standard Model of elementary particles, which of the following is NOT a composite object?

A. Muon
B. Pi-meson
C. Neutron
D. Deuteron
E. Alpha particle

(GR9677 #63)

Solution:

A.TRUE
Muon is a lepton. Leptons, along with quarks, are considered the fundamental particles.

B. FALSE
Pi-Meson consists of a quark and its antiparticle. Moreover, a pi-meson is a hadron. Hadrons interact with the strong-force, and all of them are composed of combinations of quarks. (The fundamental particles are classified as quarks and leptons.)

C. FALSE
A neutron is made up of 3 quarks.

D. FALSE
A deuteron consists of a proton and a neutron. (tritium is two neutrons and a proton, while regular Hydrogen is just an electron and proton).

E. FALSE
An alpha particle consists of electrons and protons and neutrons.

Answer: A

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

Quantum Mechanics - Wave Function

A system containing two identical particles is described by a wave function of the form

$\psi= \frac{1}{\sqrt{2}} \left[ \psi_\alpha(x_1)\psi_\beta(x_2)+ \psi_\beta(x_1)\psi_\alpha(x_2)\right ]$

Where x₁ and x₂ represent the spatial coordinates of the particles and α and β represent all the quantum numbers, including spin, of the states that they occupy. The particles might be

A. Electrons
B. Positrons
C. Protons
D. Neutrons
E. Deuterons

(GR8677 #89)

Solution:

Wave function: $\psi= \frac{1}{\sqrt{2}} \left[ \psi_\alpha(x_1)\psi_\beta(x_2)\pm \psi_\beta(x_1)\psi_\alpha(x_2)\right ]$

Symmetric function (+ sign): $\psi_{\alpha\beta}=\psi_{\beta\alpha}$

→ obey Bose-Einstein statistics → bosons

Anti-symmetric function (−sign): $\psi_{\alpha\beta}=-\psi_{\beta\alpha}$
→ obey Fermi-Dirac statistics → fermion

Electrons and positron (anti-elecron) → fermion

Protons and neutron → fermionic hadrons

composite particles (hadron)
composed of 3 fermionic quarks

Deuterons → bosons

nucleus of deuterium, an isotope of hydrogen
composed of a neutron (spin 1/2) and a proton (spin 1/2), total spin = 1

Answer: E