Problem 117 - A Complete Resource Book in Chemistry for JEE Main

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

Step-by-Step Solution

Answer

Statements (a), (b), and (c) are correct, while statement (d) is incorrect.

Step 1: Analyze Statement (a)

The decay constant, often denoted by \( \lambda \), describes the probability of a nucleus decaying per unit time. This property is intrinsic to the material and is not affected by external factors such as temperature or pressure. Hence, statement (a) is correct.

Step 2: Analyze Statement (b)

Nuclear isomers are nuclei with the same number of protons and neutrons but in different energy states. Thus, both the proton and neutron numbers are the same, but the energy levels differ. Therefore, statement (b) is correct.

Step 3: Analyze Statement (c)

The decay constant \( \lambda \) is a characteristic of a radioactive substance and does not depend on the size of the sample or the amount of substance present. Therefore, statement (c) is correct.

Step 4: Analyze Statement (d)

The decay constant is a measure of an intrinsic property of the nucleus and is generally not affected by external conditions such as temperature changes. The statement that the decay constant decreases with temperature is incorrect. Thus, statement (d) is incorrect.

Key Concepts

Decay Constant

The decay constant, denoted by \( \lambda \), is a key concept in understanding radioactive decay. It represents the probability that a given nucleus will decay in a unit of time. This constant is a unique characteristic of each type of radioactive material and relates directly to the stability of the nucleus. A higher decay constant means that the nuclei of the substance are more likely to decay quickly. An important aspect of the decay constant is its independence from external factors:

• The decay constant remains constant regardless of the sample size, which means it is unaffected by the amount of radioactive material present.
• Unlike many chemical reactions that are dependent on temperature or pressure variations, the decay constant remains unchanged by these external conditions. This makes radioactive decay a useful process in various fields requiring precise time measurement, like radiometric dating.

The robustness of the decay constant allows for predictable and reliable behavior when studying radioactive materials.

Nuclear Isomers

Nuclear isomers are a fascinating aspect of nuclear physics. They are nuclei that share the same number of protons and neutrons but exist in different energy states. Despite having the same composition in terms of protons and neutrons, they can exhibit varying properties due to these distinct energy configurations:

• Nuclear isomers can differ in their half-lives, which is the time required for half the nuclei in a sample to decay, due to different energy levels.
• This phenomenon is valuable in nuclear medicine, as different isomers can be used for diagnostic or therapeutic purposes depending on their stability and energy state.

Understanding nuclear isomers is crucial because it enables scientists to exploit their properties for specific applications while acknowledging their identical composition.

Intrinsic Properties of Nuclei

The intrinsic properties of nuclei are fundamental to understanding nuclear behavior and stability. These properties include:

• The decay constant, which as previously mentioned, is an intrinsic characteristic unaffected by external conditions.
• Binding energy, which indicates the energy required to disassemble a nucleus into its constituent protons and neutrons.
• Mass number, which is the total number of protons and neutrons in a nucleus, influencing its stability.

These intrinsic properties are vital because they dictate how a nucleus will behave independently of the environment, making them a central point of study in nuclear physics and related applications.

Temperature and Pressure Effects

Temperature and pressure are critical factors in many chemical and physical processes, but their influence is negligible when it comes to nuclear decay. Unlike chemical reactions, which often depend heavily on temperature and pressure:

• Nuclear decay, governed by the decay constant, is not influenced by changes in temperature or pressure. This makes nuclear processes highly reliable and predictable.
• This independence stems from the fact that nuclear decay deals with interactions within the nucleus, while temperature and pressure typically affect outer electron cloud interactions.

Thus, the unchanging nature of nuclear decay under varying temperature and pressure conditions ensures consistent results in experiments and practical applications. Students should appreciate this stability as it significantly simplifies calculations and forecasts involving radioactive substances.