Unit 12: Nuclear and Particle Physics — Short Questions

Common Different isotopes of a given element have the same number of protons (atomic number) in their atomic nuclei, which means they have the same chemical properties.
Different: They differ in the number of neutrons in their nuclei, resulting in different atomic masses (or mass numbers). This difference in neutron number affects their physical properties, such as mass, density, and stability.

To identify the element Nucleons = protons + neutrons = 87 = atomic mass
So, Protons = A - N = 87 - 50 = 37
The element with atomic number 37 is Rubidium (37 Rb)

Similarities (i) Both are fundamental forces in nature.
(ii) Both forces act between particles.
(iii) Both obey conservation of energy and momentum.
(iv) Both follow inverse square law.
Differences:
(i) Range: Strong nuclear force has a short range (acts over nuclear distances, ≈ 10^-15 m), while electric force has a long range (acts over much larger distances).
(ii) Strength: Strong nuclear force is much stronger than electric force at short ranges, but electric force dominates at larger distances.
(iii) Charge dependence: Strong nuclear force acts between quarks and nucleons (no charge dependence), while electric force acts between charged particles dependent on charge.
(iv) Effect on Protons/Neutrons: The strong nuclear force holds quarks together inside protons/neutrons and binds nucleons in the nucleus, overcoming electric repulsion between positively charged protons.

(a) This represents beta minus decay, where a neutron decays into a proton, emitting an electron and antineutrino. The atomic number increases by one and mass number remains same. The resulting nucleus is scandium (⁴⁵Sc).
(b) In 58₂₉Cu → 58₂₉Cu+γ. Since emission of γ ray photon neither change its charge number nor mass number so, only the energy state will change (i.e. cu )

In beta plus (β⁺) decay (positron emission), a proton in the nucleus is converted into a neutron, a positron (e⁺), and a neutrino (ν):
P → n + e⁺ + ν
A neutrino is released in positron emission to conserve energy and momentum.

Fermions (i) Particles with half-integer spin (1/2, 3/2, etc.).
(ii) Follow fermi-Dirac statistics.
(iii) Include particles like electrons, protons, neutrons, and quarks.
(iv) Obey the Pauli exclusion principle (no two fermions can occupy the same quantum state).
Bosons:
(i) Particles with integer spin (0, 1, etc.).
(ii) Follow Bose-Einstein statistics.
(iii) Include particles like photons, gluons, and mesons.
(iv) Do not obey the Pauli exclusion principle (multiple bosons can occupy the same quantum state).

The strong nuclear force holds the nucleus together by binding protons and neutrons, overcoming the repulsion between positively charged protons.
The strong force is due to particles called gluons, which are exchanged between quarks. Quarks are building blocks of protons and neutrons.

No, pair production requires a photon energy of at least 1.022 MeV (2 × 0.511 MeV, the rest mass energy of an electron positron pair).
Since 20 keV is much less than 1.022 MeV, pair production is not possible with a photon of this energy.

Beta particle and electron are essentially the same particle. The difference lies in their origin:
(i) Electron: Typically refers to constituent of atom, orbiting the nucleus.
(ii) Beta particle: Specifically refers to electrons (β⁻) or positrons (β⁺) emitted from the nucleus during radioactive decay.
So, all beta particles are electrons or positron, but not all electrons are beta particles.

A proton and a neutron can convert to each other through weak nuclear force.
(i) Proton to neutron:
Through beta plus (β⁺) decay a proton can convert into a neutron.
p → n + e⁺ + ν
(ii) Neutron to Proton:
Through beta minus (β⁻) decay, a neutron can convert into a proton.
n → p + e⁻ + v̄

Beta decay has a continuous energy spectrum because the energy is shared between the beta particle and the neutrino (or antineutrino) in varying proportions. Each decay event distributes the energy differently, resulting in a range of energies for the beta particles.
Alpha decay has a discrete energy spectrum because the alpha particle is emitted with a specific energy, determined by the difference in nuclear binding energies between the parent and daughter nuclei. Since alpha decay typically involves a two-body decay (parent nucleus → alpha particle + daughter nucleus), the alpha particle carries all the energy.

Hadrons (i) Particles that interact via the strong nuclear force.
(ii) Composed of quarks.
(iii) Examples:
Protons (p), neutrons.
Pions (π mesons)
Leptons:
(i) Particles that do not interact via the strong nuclear force.
(ii) Fundamental particles, not composed of quarks.
(iii) Examples:
Electrons (e⁻)
Muons (μ)
Neutrinos (ν)

An electron-positron pair cannot decay into a single photon because it would violate the law of conservation of momentum.
As the total linear momentum is zero before conversion. So, two photons should be emitted to move in opposite direction with equal magnitude of momentum to conserve momentum.
The most common process is:
e⁻ + e⁺ → γ + γ

The Higgs boson is linked to the Higgs field, a field that permeates space. Particles gain mass by interacting with this field. The more a particle interacts with the Higgs field, the more mass it acquires. The discovery of the Higgs boson confirmed this mechanism, explaining why some particles like w, w' and z bosons have mass while others (like photons) do not.

Mesons are a type of hadron, which are particles made up of one quark and one antiquark. They are bosons (integer spin particles) and interact via the strong nuclear force.
Examples:
(i) Pions (π⁺, π⁻, π⁰)
(ii) Kaons (K⁺, K⁻, K⁰)
Mesons are unstable and decay quickly into other particles.

Atomic Number The number of protons or electrons present in any atom is called its atomic number. Atomic number is also called charge number. It is usually denoted by a letter Z.
Mass Number:
The sum of protons and neutrons present in the nucleus of an atom is called its mass number. It is also called as nucleon number and is denoted by a letter A.

Atomic number 92
Number of neutrons 143
Number of electrons 92
Charge Number 92

²³⁵₉₂U and ²³⁸₉₂U have some charge number i.e. Z = 92. However, the number of neutrons in ²³⁵₉₂U are N = A – Z = 235 – 92 = 143
The numbers of neutrons in ²³⁸U are N = A – Z = 238 – 92 = 146
Hence, the ²³⁵U and ²³⁸U differs by three (3) neutrons. It shows that they are isotopes containing same number of electrons or protons i.e. charge number Z but mass number A is different.

Henri Becquerel discovered the phenomena of radioactivity in 1896 in Uranium. It was found that it emits three type of radiations known as α, β and γ rays.

When a nucleus emits an α – particle (also called α – decay)' its mass number decreases by 4 while charge number by 2. An α – decay of radium ₈₈Ra is converted into
Radon ²²⁶₈₈Ra → ²²²₈₆Rn is given as follow:
²²⁶Ra → ²²²Ra + ⁴He

It is a high frequency electromagnetic radiation. Its origin is the nucleus. When an excited nucleus returns back to its ground state, it give rise to emission of γ-radiations. The mass number and charge number remain same during γ-ray emission.

(i) They are massive and have intense ionizing power during interaction with the matter.
(ii) Due to their large mass, their penetration is very small.

(i) Beta particles are regarded as electrons. Due to smaller charge as compared to α - particles, the ionizing property of β - particles is about 100 times less than that of α - particle
(ii) β - particle can radiate energy when are slowed down by electric field of the charged particles.

(i) Gamma rays at very high energy (≥ 1.02 MeV) can cause phenomena of pair – production.
(ii) At intermediate energies they can show Compton scattering effect
(iii) At low energies (e.g. < 0.5 MeV) they can remove electrons from only metallic surface through photoelectric effect.

The fraction of the total is number of atoms decayed per unit time is called decay constant. It is denoted by λ and it measured in sec⁻¹

Hadrons are not elementary particles. They are composed of other elementary particles called quarks. The examples of hadrons are protons, neutrons, mesons etc. they experience strong nuclear force.
Leptons are the elementary particles. They do not experience strong nuclear force. Family of leptons include electrons, Muons and neutrinos.

Mesons are bosons, not fermions.
Reason: Mesons are composed of one quark and one antiquark, resulting in an integer spin (0,1,2….), which classifies them as bosons.

Alpha particles (2 protons + 2 neutrons) are emitted instead of four separate nucleons because:
(i) Binding energy: The alpha particle has a high binding energy per nucleon, making it a stable and energetically favorable configuration.
(ii) Strong nuclear force: The strong nuclear force holds the two protons and two neutrons together in the alpha particle, making it more likely to be emitted as a single unit.
Emitting an alpha particle is more energetically favorable than emitting four separate nucleons, which would require more energy to overcome the strong nuclear force.

Alpha decay is generally more energetic than beta decay due to the larger mass and charge of alpha particles, resulting in higher kinetic energy release.

Given energy of gamma ray photon:
1.5 MeV = 1.5 × 10⁶ × 1.6 × 10⁻¹⁹ J
= 2.4 × 10⁻¹³ J
As (1₈ᵥ = 1.6 × 10⁻¹⁹ J)
Frequency (f): ?
E = hf
f = E / h
= (2.4 × 10⁻¹³ J) / (6.626 × 10⁻³⁴ Js)
= 3.62 × 10²⁰ Hz
Wavelength (λ):
λ = c / f
= (3 × 10⁸ m/s) / (3.62 × 10²⁰ Hz)
= 8.28 × 10⁻¹³ m
Momentum (p):
p = E /c
= (2.4 × 10⁻¹³ J) / (3 × 10⁸ m/s)
= 8 × 10⁻²² kg m/s

Alpha particles don't make physical contact with the nucleus when headed directly towards it due to the electrostatic repulsion between the positively charged alpha particle and the positively charged nucleus.
As the alpha particle approaches the nucleus, the electrostatic repulsive force increases, causing the alpha particle to be repelled or deflected before it can physically touch the nucleus.

See Q.4 of theory

See Q.5 of theory.

See Q.3 of theory.

See Q.4 of theory.

See Q.4 of theory.

See Q.8 of theory.

See Q.2 of theory.

See Q.7 of theory.