Problem 84 - A Complete Resource Book in Chemistry for JEE Main

Question

Observe the following statements regarding isotopes I. \(\mathrm{K}^{39}\) and \(\mathrm{Ca}^{40}\) are isotones II. Nuclides having different atomic number (Z) and mass number (a) but same number of neutrons (n) are called isotones. III. \(\mathrm{F}^{19}\) and \(\mathrm{Na}^{23}\) are isotones. The correct answer is (a) only I and II are correct (b) I, II and III are correct (c) only I and III are correct (d) only II and III are correct

Step-by-Step Solution

Answer

Correct answer is (a) only I and II are correct.

Step 1: Understand Isotones

Isotones are nuclides with the same number of neutrons. Recall that the neutron number (n) is calculated as the difference between mass number (A) and atomic number (Z). Therefore, isotones have: \( n = A - Z \).

Step 2: Evaluate Statement I

For \( \mathrm{K}^{39} \) and \( \mathrm{Ca}^{40} \):- Potassium (\( \mathrm{K} \)) has an atomic number \( Z = 19 \), so its neutron number is: \( 39 - 19 = 20 \).- Calcium (\( \mathrm{Ca} \)) has an atomic number \( Z = 20 \), so its neutron number is: \( 40 - 20 = 20 \).Both have the same number of neutrons (20), hence they are isotones.

Step 3: Evaluate Statement II

Statement II defines isotones as nuclides with different atomic numbers and mass numbers but the same number of neutrons. This matches the definition outlined in Step 1 and hence is a correct definition.

Step 4: Evaluate Statement III

For \( \mathrm{F}^{19} \) and \( \mathrm{Na}^{23} \):- Fluorine (\( \mathrm{F} \)) has an atomic number \( Z = 9 \), so its neutron number is: \( 19 - 9 = 10 \).- Sodium (\( \mathrm{Na} \)) has an atomic number \( Z = 11 \), so its neutron number is: \( 23 - 11 = 12 \).These have different numbers of neutrons (10 and 12, respectively), so they are not isotones.

Key Concepts

Nuclides

Nuclides are essentially different types of atomic nuclei. Each nuclide is characterized by its number of protons and neutrons. While the term "nuclide" is often used interchangeably with "isotope," they are not exactly the same. An isotope refers to variants of a particular element that have the same number of protons but different numbers of neutrons.
In contrast, nuclides can refer to any atomic nucleus with a specific number of protons and neutrons, regardless of whether it is part of the same element. This makes nuclides a broader concept. For instance:

• When scientists discuss isotopes, they are focusing on variants of a single element.
• However, when discussing nuclides, the focus can include completely different elements.

This distinction is important when dealing with concepts like isotones, where the counting of neutrons rather than protons is essential.

Neutrons

Neutrons are subatomic particles found in the nucleus of an atom, alongside protons. While protons have a positive charge, neutrons have no charge and are electrically neutral, hence their name. The number of neutrons in an atom can significantly affect its properties.
The neutron number is integral for defining different types of atomic behavior. It is calculated by subtracting the atomic number (the number of protons) from the mass number (the total number of protons and neutrons). This calculation is essential for identifying isotones, as isotones share the same number of neutrons but can have different atomic numbers and mass numbers.

• For example, in nuclides that are isotones, the neutron count remains constant while other aspects like the number of protons can vary.

This concept helps categorize elements and understand their nuclear properties.

Atomic Number

The atomic number is the number of protons found in the nucleus of an atom and is denoted by the symbol "Z." It essentially defines the identity of an element, as each element on the periodic table has a unique atomic number.
An element's atomic number determines many of its chemical properties and its place in the periodic table. For instance:

• Hydrogen, with an atomic number of 1, is the simplest element.
• With a higher atomic number, Uranium (92) is heavier and more complex.

Understanding the atomic number is crucial when studying isotones because, despite sharing the same neutron count, isotones always have different atomic numbers. This difference is what distinguishes them from isotopes.

Mass Number

The mass number, represented by the symbol "A," is the total number of protons and neutrons in an atomic nucleus. It is a whole number, giving a rough measure of the atom's total mass.
Unlike atomic number, which strictly identifies an element, mass number varies among isotopes and isotones of the same element. For example, when comparing isotones, each nuclide will have a unique atomic number and mass number, but the same number of neutrons.

• Mass number aids in determining isotopic mass and understanding nuclear stability.
• This concept is also vital in radioactivity, where alterations in mass number can signal decay processes.

It's especially useful for calculating the neutron number by subtracting the atomic number from the mass number.