Problem 144 - A Complete Resource Book in Chemistry for JEE Main

Question

A photon of hard \(\gamma\) radiation knocks a proton out of \({ }_{12} \mathrm{Mg}^{44}\) nucleus to form (a) the isotope of parent nucleus (b) the isobar of parent nucleus (c) the nuclide of \({ }_{11} \mathrm{Na}^{23}\) (d) the isobar of \(_{11} \mathrm{Na}^{23}\)

Step-by-Step Solution

Answer

(a) \( ^{43}_{11}\text{Al} \), (b) \( ^{44}_{20}\text{Ca} \) or \( ^{44}_{18}\text{Ar} \), (c) \( ^{23}_{11}\text{Na} \), (d) \( ^{23}_{12}\text{Mg} \).

Step 1: Understanding the Problem

The problem requires identifying various types of isotopes or isobars related to a nuclear reaction where a hard gamma photon knocks a proton out of a magnesium nucleus. This will help us determine the changes in the atomic and mass numbers and the resulting isotopes, isobars, or nuclides.

Step 1: Forming the Isotope of the Parent Nucleus

Given the Mg^{44} nucleus, knocking out a proton changes it to an aluminium nucleus. After losing a proton (and balancing with an neutron), the new nucleus is _{11}Al^{43}, so it is the isotope of the parent.

Step 2: Finding Isobar of the Parent Nucleus

An isobar has the same number of nucleons (mass number) but a different proton (atomic) number. The parent Mg^{44} has a mass number of 44, so an isobar could be _{20}Ca^{44} or _{18}Ar^{44}.

Step 3: Identifying Nuclide of \({ }_{11} \mathrm{Na}^{23}\)

The nuclide that corresponds to _{11}Na^{23} is identical in both atomic number and mass number, which is _{11}Na^{23} itself.

Step 4: Determining Isobar of \(_{11} \mathrm{Na}^{23}\)

The isobar of _{11}Na^{23} must share the same mass number of 23 but different atomic number; an example could be _{12}Mg^{23}.

Key Concepts

Gamma Radiation

Gamma radiation is a high-energy form of electromagnetic radiation, often emitted during radioactive decay processes in nuclear reactions. It has incredibly short wavelengths and high frequencies, which gives it significant penetration power. This makes gamma rays useful in medical imaging and cancer treatment but also means they must be handled with caution due to their potential to damage living cells.
Understanding gamma radiation is crucial in nuclear physics as it is often involved in reactions where nuclei rearrange or decay, releasing energy in the form of photons. In the context of gamma rays knocking out a proton from a nucleus, as seen in the exercise, gamma radiation can induce changes in the atomic structure, leading to different isotopes or elements being formed.

Isotopes

Isotopes are variants of a particular chemical element that have the same number of protons but differ in the number of neutrons. This means isotopes of an element have the same atomic number but different mass numbers.
For example, in the given exercise, when a gamma ray knocks a proton out of a magnesium nucleus ( _{12}Mg^{44}), the resulting nucleus is _{11}Al^{43}. Here, aluminium is a different element altogether, but adjusting this scenario to focus on isotopes of the parent element, isotopes would instead involve variations of magnesium itself, like _{12}Mg^{43}, where the neutron count changes but magnesium remains the parent element.

Isobars

Isobars are nuclei that have the same mass number but different atomic numbers, meaning their total number includes a different combination of protons and neutrons. In nuclear reactions, identifying isobars is crucial for understanding how elements can interrelate while keeping the mass constant.
The exercise shows that the isobar of the parent nucleus ( _{12}Mg^{44}) could be _{20}Ca^{44} or _{18}Ar^{44}, each having the same mass number but differing in proton count. Similarly, for _{11}Na^{23}, an isobar like _{12}Mg^{23} shows how shifting just one proton still adheres to the rule of identical mass numbers.

Nuclides

Nuclides are distinct species of atoms that have a particular number of protons and neutrons. Each nuclide is identified by its atomic number, mass number, and nuclear energy state. Understanding nuclides involves recognizing specific arrangements within an atom's nucleus, which is critical for comprehending nuclear reactions.
In the exercise, the 'nuclide of _{11}Na^{23}' remains _{11}Na^{23} itself, underscoring that in some scenarios, the nuclide designation stays unchanged because both the atomic and mass numbers remain constant. This stability makes certain nuclides key standards in nuclear processes and applications.