Question

Which of the following statement is/are correct? (a) The decay constant is independent of external factors like temperature and pressure (b) Nuclear isomers have same number of protons and neutrons (c) The decay constant is independent of the amount of the substance used (d) The value of decay constant generally decreases with the rise in temperature

Short answer

Statements (a), (b), and (c) are correct.

Step-by-step solution

Understand Decay Constant

The decay constant, often denoted by \( \lambda \), represents the probability per unit time that a given nucleus will decay. It is a fundamental property of a radioactive substance.

Analyze Statement (a)

Statement (a) suggests that the decay constant is independent of external factors like temperature and pressure. This is true, as radioactive decay is a nuclear process unaffected by such external conditions.

Analyze Statement (b)

Statement (b) claims that nuclear isomers have the same number of protons and neutrons. Nuclear isomers are nuclei with the same atomic number and mass number but different energy states, usually involving different configurations of their nucleons. This statement is correct.

Analyze Statement (c)

Statement (c) states that the decay constant is independent of the amount of substance. This is correct because \( \lambda \) is a property of the radioactive isotope itself, not affected by the amount of the sample.

Analyze Statement (d)

Statement (d) suggests that the decay constant decreases with an increase in temperature. This is false because the decay constant is unaffected by temperature; it remains constant regardless of temperature changes.

Conclusion

From the analysis of each statement, statements (a), (b), and (c) are correct.

Key concepts

Decay Constant

The decay constant, represented by the Greek letter \( \lambda \), is a crucial parameter in the field of radioactive decay. It reflects the likelihood that a particular radioactive atom will decay in a given time period.
One fascinating thing about the decay constant is that it relies solely on the properties of the radioactive substance itself. This means that even if external conditions change, such as temperature or pressure, the decay constant remains unchanged. Radioactive decay is inherently a nuclear process, so factors like heat or atmospheric pressure do not have any effect on it.
The decay constant is an intrinsic characteristic of each radioactive isotope, similar to a fingerprint that defines its stability and behavior during the decay process. No matter how much substance is present, \( \lambda \) will not alter, making it a reliable measure across different sample sizes.

Nuclear Isomers

In the realm of nuclear physics, nuclear isomers are nuclei which share the same number of protons and neutrons, but exhibit different energy states. This unique state difference arises from the varying arrangements of nuclear particles or nucleons within the nucleus.
Despite having identical atomic and mass numbers, these isomers display distinct physical properties. For instance, they might emit gamma rays of different energies, showcasing their difference in energy levels. What sets nuclear isomers apart is this ability to exist in metastable states, which are more stable than the excited state but less stable than the ground state.
Therefore, unlike isotopes, which differ in neutron number, nuclear isomers maintain identical numbers of both protons and neutrons. Their distinctiveness lies solely in their nuclear configurations and resultant energy states.

External Factors in Nuclear Reactions

Nuclear reactions, including radioactive decay, are highly resilient against changes in external environmental factors such as temperature, pressure, or chemical state. This is because nuclear reactions deal with the nucleus of the atom, which is a region unaffected by the electron shell interactions that typically respond to such conditions.
For example, altering the pressure or increasing the temperature will affect the physical state of a substance—like turning ice to water—but such changes do not influence the rate at which a radioactive nucleus decays. Consequently, the decay constant, \( \lambda \), remains stable under varying external conditions.
Understanding this resistance to environmental factors is crucial for both using and studying radioactive materials. For instance, in nuclear power plants or radioactive dating, this property ensures predictable and reliable decay rates regardless of the surrounding environment.