Problem 69 - Master Resource Book in JEE Main Physics

Question

Tritium is an isotope of hydrogen whose nucleus Triton contains 2 neutrons and 1 proton. Free neutrons decay into \(p+\bar{e}+\bar{v}\). If one of the neutrons in Triton decays, it would transform into \(\mathrm{He}^{3}\) nucleus. This does not happen. This is because [NCERT Exemplar] (a) Triton energy is less than that of a \(\mathrm{He}^{3}\) nucleus. (b) The electron created in the beta decay process cannot remain in the nucleus. (c) both the neutrons in trition have to decay simultaneously resulting in a nucleus with 3 protons, which is not a \(\mathrm{He}^{3}\) nucleus. (d) because free neutrons decay due to external perturbations which is absent in a triton nucleus.

Step-by-Step Solution

Answer

The correct option is (a). Triton energy is less than that of a Helium-3 nucleus.

Step 1: Understanding Triton Composition

Triton is the nucleus of Tritium, which is an isotope of hydrogen. It contains one proton and two neutrons. If one neutron decays, the balance might seem to shift towards Helium-3, which contains two protons and one neutron.

Step 2: Analyzing Neutron Decay

A free neutron decays into a proton, an electron, and an antineutrino. This process is typical when neutrons are isolated and not part of a stable nucleus. The presence of other nucleons can stabilize the neutron.

Step 3: Helium-3 Nucleus Composition

Helium-3 (He^{3}) has 2 protons and 1 neutron. If a neutron in Triton decays, one might think it could create Helium-3; however, there are factors preventing this transformation.

Step 4: Checking Energy and Stability

In this case, consider why the decay doesn't occur: the energy configuration in Triton might be more favorable compared to that of a Helium-3 nucleus. Energetically stable configurations resist transformations.

Step 5: Choose the Correct Option

After analyzing the possibilities, review the options. The ongoing constraint is that Triton energy may be lower than a Helium-3 nucleus, preventing decay. Therefore, (a) is the conclusion.

Key Concepts

Isotopes

An isotope is a variant of a chemical element, which shares the same number of protons but differs in the number of neutrons. The number of neutrons affects the atomic mass and can influence the stability of the nucleus. For example:

• Hydrogen has three isotopes: Protium (no neutrons), Deuterium (one neutron), and Tritium (two neutrons).
• Isotopes of an element chemically behave the same due to their similar proton number, but their physical properties may be notably different.
• Tritium is an isotope of hydrogen known for its radioactivity due to the presence of two neutrons in its nucleus.

This diversity in isotopes provides a unique landscape for studying reactions and decay processes in nuclear physics.

Beta Decay

Beta decay is a radioactive process where an unstable neutron transforms into a proton, emitting a beta particle (electron) and an antineutrino. This process is crucial in understanding how nuclei achieve stability. During beta decay:

• A neutron becomes a proton within the nucleus.
• The emitted electron, known as a beta particle, carries away negative charge.
• An antineutrino is also released, a very light particle conveying little mass and energy.

This decay increases the atomic number by one, transforming the element into its subsequent higher neighbor on the periodic table. For isotopes like Tritium undergoing decay, this could hypothetically change it into Helium-3 if external conditions favored such a transition.

Nuclear Stability

Nuclear stability is a key concept in nuclear physics that determines whether a nucleus will undergo decay. It depends on the ratio of protons to neutrons and the energy associated with these particles.

• Nuclei are more stable when they achieve a certain ratio of neutrons to protons.
• Stable nuclei resist decay processes that would alter their composition.
• Energy levels in a nucleus contribute to its overall stability; lower energy configurations are often more stable.

In the context of Tritium, despite the presence of two neutrons, the isotope remains stable enough that neutron decay into Helium-3 doesn't happen under natural conditions due to these stability factors.

Helium-3

Helium-3 is a light, stable isotope of helium with two protons and one neutron, differing from the more common Helium-4. Its properties:

• Helium-3 is non-radioactive and found in trace amounts on Earth.
• Its unique composition makes it useful for research in cryogenics and quantum computing.
• In nuclear reactions, Helium-3 plays a role as a potential fuel source due to its involvement in fusion processes.

While Tritium might seem a candidate to transform into Helium-3 through neutron decay, the absence of such a process highlights the nuanced balance of energy and nuclear forces in determining possible transformations.

Tritium

Tritium, or Hydrogen-3, is a radioactive isotope of hydrogen. It contains:

• One proton, similar to all hydrogen isotopes.
• Two neutrons, which are responsible for its radioactivity.
• A relatively short half-life of about 12 years, making it unstable over time.

Tritium is used in various applications:

• In nuclear fusion reactions, as it can serve as a high-energy fuel source.
• For labeling in biochemical research due to its radioactivity.
• In self-illuminating gadgets like watch dials and emergency exit signs.

Understanding Tritium and its characteristics helps in explaining why despite having the potential for beta decay, the transformation to Helium-3 does not naturally occur due to the energy dynamics and stability concerns described above.