Question

The nuclear of which of following Pairs of nuclei are isotones (A) \({ }_{34} \mathrm{Se}^{74},{ }_{31} \mathrm{Ca}^{71}\) (B) \(_{42} \mathrm{Mo}^{92}, 40 \mathrm{Zr}^{92}\) (C) \({ }_{38} \mathrm{Sr}^{81}, 38 \mathrm{Sr}^{86}\) (D) \({ }_{20} \mathrm{Cd}^{40}, 16 \mathrm{~S}^{32}\)

Short answer

The pair of isotones is (A) \({ }_{34} \mathrm{Se}^{74},{ }_{31} \mathrm{Ca}^{71}\), as both nuclei have the same neutron number (N = 40).

Step-by-step solution

Calculate neutron numbers for each pair

For pair (A) \({ }_{34} \mathrm{Se}^{74},{ }_{31} \mathrm{Ca}^{71}\), neutron numbers are: N1 = \(A_{Se} - Z_{Se}\) = 74 - 34 = 40 N2 = \(A_{Ca} - Z_{Ca}\) = 71 - 31 = 40 For pair (B) \(_{42} \mathrm{Mo}^{92}, 40 \mathrm{Zr}^{92}\), neutron numbers are: N1 = \(A_{Mo} - Z_{Mo}\) = 92 - 42 = 50 N2 = \(A_{Zr} - Z_{Zr}\) = 92 - 40 = 52 For pair (C) \({ }_{38} \mathrm{Sr}^{81}, 38 \mathrm{Sr}^{86}\), neutron numbers are: N1 = \(A_{Sr81} - Z_{Sr}\) = 81 - 38 = 43 N2 = \(A_{Sr86} - Z_{Sr}\) = 86 - 38 = 48 For pair (D) \({ }_{20} \mathrm{Cd}^{40}, 16 \mathrm{~S}^{32}\), neutron numbers are: N1 = \(A_{Cd} - Z_{Cd}\) = 40 - 20 = 20 N2 = \(A_{S} - Z_{S}\) = 32 - 16 = 16

Find the pair of isotones

Now, comparing the neutron numbers for the given pairs: - Pair (A): N1 = 40 and N2 = 40, neutron numbers are equal, which indicates these nuclei are isotones. - Pair (B): N1 = 50 and N2 = 52, neutron numbers are not equal, which indicates these nuclei are not isotones. - Pair (C): N1 = 43 and N2 = 48, neutron numbers are not equal, which indicates these nuclei are not isotones. - Pair (D): N1 = 20 and N2 = 16, neutron numbers are not equal, which indicates these nuclei are not isotones. Only pair (A) has equal neutron numbers, so the correct answer is pair (A): \({ }_{34} \mathrm{Se}^{74},{ }_{31} \mathrm{Ca}^{71}\).

Key concepts

Neutron Number

The neutron number is a fundamental concept in nuclear physics. It represents the number of neutrons present in a nucleus. Neutrons along with protons, which are called nucleons, form the core of an atom. While protons determine the chemical element of an atom, neutrons play a critical role in the characteristics of isotopes and isotones.
To calculate the neutron number, you simply subtract the atomic number (Z) from the mass number (A) of an atom. This is mathematically expressed as: \[ \text{Neutron Number} (N) = A - Z \]

• A is the mass number, which is the total number of protons and neutrons in the nucleus.
• Z is the atomic number, which is the number of protons in the atom.

Understanding the neutron number helps in identifying isotones, which are nuclei sharing the same number of neutrons but may have different chemical properties due to differing numbers of protons.

Nuclear Physics

Nuclear physics explores the constituents and interactions at the core of the atom, primarily focusing on the behavior of protons and neutrons. These tiny components, known as nucleons, are held together in the nucleus by the strong nuclear force, which is one of the four fundamental forces in nature. Insights from nuclear physics have led to advanced technologies, including nuclear energy and medical imaging techniques.
Key topics include:

• Atomic Nucleus Structure: Exploring how nucleons are arranged inside the nucleus and the forces at play.
• Radioactivity: Analyzing spontaneous nuclear changes, including alpha, beta, and gamma decay.
• Nuclear Reactions: Understanding processes like fission and fusion which release a considerable amount of energy.

Nuclear physics also helps us understand diverse phenomena such as the synthesis of elements in stars and the functioning of nuclear reactors.

Isotopes vs Isotones

Both isotopes and isotones are terms used to describe nuclei, but they refer to distinct characteristics. Isotopes are nuclei that have the same number of protons but differ in the number of neutrons. This variation in neutron number leads to different mass numbers for isotopes of the same element. For example, carbon-12 and carbon-14 are isotopes of carbon, sharing the same atomic number but differing in neutron number.
In contrast, isotones have the same number of neutrons but differ in both their atomic and mass numbers. This means they can be completely different elements. For example:

• Pair (A) from the exercise:
  • \(^{74}_{34}Se\) has 40 neutrons.
  • \(^{71}_{31}Ca\) also has 40 neutrons.

Isotones like these share neutron numbers but belong to different chemical elements. The comparison between isotopes and isotones is crucial to understanding the complexity of nuclear structures and the behavior of nuclei under various physical and chemical conditions.