Problem 17 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

When a nucleus reverts from an excited state to the ground state, the energy difference between the two states is emitted as (a) \(\alpha\) -particle (b) \(\beta\) -particle (c) \(\gamma\) -rays (d) neutrino

Step-by-Step Solution

Answer

The energy difference between the two states is emitted as (c) \(\gamma\)-rays.

Step 1: Understand the process of de-excitation

When an atomic nucleus transitions from an excited state to the ground state, it releases energy to return to a lower energy level. This energy can be emitted in various forms depending on the type of transition and the involved particles.

Step 2: Identify the type of emission associated with energy transitions

In the case of a nucleus releasing excess energy without changing its charge or mass number, the energy is typically emitted in the form of electromagnetic radiation. This energy release does not involve the emission of particles with mass, such as alpha or beta particles, or neutrinos, which are involved in other types of nuclear reactions.

Step 3: Determine the correct form of energy release

The emission that corresponds to the energy difference when reverting from an excited state to the ground state without altering the nucleus structure in terms of the number of protons or neutrons is gamma radiation, which is pure energy in the form of high-frequency electromagnetic waves.

Key Concepts

Gamma Radiation

Gamma radiation is a type of electromagnetic radiation that is incredibly energetic, characterized by its high frequency and short wavelength. Unlike alpha and beta particles which consist of actual matter, gamma rays are pure energy, akin to X-rays but typically more energetic. These rays are emitted during the de-excitation of a nucleus, which occurs when the nucleus transitions from a higher energy state to a lower energy state without changing its number of protons or neutrons.

Gamma rays can penetrate through most materials, which is why they require heavy shielding, such as lead or concrete, to protect against them. Due to their penetrating power and the fact that they can damage living tissue, gamma rays can be both useful and harmful. They are widely used in medical treatments, such as in cancer radiotherapy to kill malignant cells, and in imaging techniques, like gamma-ray imaging to diagnose illnesses. However, exposure to high levels of gamma radiation can cause serious health effects, including radiation sickness and increased risk of cancer.

Nuclear Excited States

In nuclear physics, an 'excited state' of a nucleus refers to any configuration of its protons and neutrons that is at a higher energy level than the ground state, which is the lowest energy state of the nucleus. Think of it like a ladder—where the ground state is the bottom rung, and any state above that is an 'excited' rung.

The transition of the nucleus to this excited state often happens after it absorbs energy from some external source, such as when it captures a neutron or is excited by a gamma ray. Each excited state is quantized, meaning they have specific, discrete energy levels. An excited nucleus is unstable, therefore it seeks to return to its ground state. In doing so, it will release the excess energy, often in the form of gamma radiation, as it makes a leap down to a lower energy rung on the ladder.

Ground State Transition

A 'ground state transition' describes the process when an atomic nucleus returns from an excited state to the ground state. This is essentially the nucleus relaxing back to its lowest energy configuration. Energy must be conserved during this process, so the energy difference between the excited state and the ground state has to go somewhere—it's emitted from the nucleus.

While ground state transitions can release energy in various forms, including particle emissions like alpha and beta particles, the transition involving gamma radiation does not emit particles with mass. Instead, the nucleus emits a gamma ray, which is a photon of high-energy electromagnetic radiation. This type of transition is usually quick, and it's a key mechanism by which radioactive materials lose their excess energy over time.