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 \((\mathrm{Z})\) 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

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

Step 1: Understand the Concept of Isotones

Isotones are nuclides with different atomic numbers but the same number of neutrons. This means that for two elements to be isotones, the number of neutrons (calculated as atomic mass - atomic number) must be the same for both.

Step 2: Evaluate Statement I

Evaluate if \(\mathrm{K}^{39}\) and \(\mathrm{Ca}^{40}\) are isotones. \(\mathrm{K}^{39}\) has \(19\) protons, so neutrons = \(39 - 19 = 20\). \(\mathrm{Ca}^{40}\) has \(20\) protons, so neutrons = \(40 - 20 = 20\). Since both have \(20\) neutrons, they are isotones.

Step 3: Evaluate Statement II

Statement II is a definition: Nuclides with different atomic numbers and mass numbers but the same number of neutrons are called isotones. This is accurate based on the definition of isotones as defined.

Step 4: Evaluate Statement III

Evaluate if \(\mathrm{F}^{19}\) and \(\mathrm{Na}^{23}\) are isotones. \(\mathrm{F}^{19}\) has \(9\) protons, so neutrons = \(19 - 9 = 10\). \(\mathrm{Na}^{23}\) has \(11\) protons, so neutrons = \(23 - 11 = 12\). Since they have different numbers of neutrons, they are not isotones.

Step 5: Identify the Correct Answer

Based on Steps 2, 3, and 4, statements I and II are correct, while statement III is incorrect. Therefore, the correct answer is option (a).

Key Concepts

Atomic Number

In simple terms, the atomic number of an element is the number of protons found in the nucleus of its atom. This unique number distinguishes one element from another and defines the very identity of the element.

The periodic table is organized by atomic numbers, so as you move from left to right across a period, the atomic number increases by one for each subsequent element. For example:

• Hydrogen has an atomic number of 1 (one proton).
• Helium has an atomic number of 2 (two protons).
• Carbon has an atomic number of 6 (six protons).

Every element is defined by its atomic number – it's never repeated across different elements. This makes it a powerful way to identify and differentiate elements in chemical reactions and other scientific studies.

Furthermore, while isotopes of an element have different numbers of neutrons, they share the same atomic number. This straightforward aspect of atomic numbers helps to easily distinguish isotopes and other similar concepts, such as isotones.

Mass Number

The mass number of an element is the total count of protons and neutrons in its atomic nucleus. This number is often used to identify isotopes of an element, since it reflects not just the atomic part of the atom but the entire nucleus.

To derive the mass number, simply add the number of protons (atomic number) to the number of neutrons. It can be represented as follows:

• Mass number = Atomic number + Number of neutrons

For example, a carbon isotope with 6 protons and 8 neutrons will have a mass number of 14. The notation for carbon-14 is often written as \[ \text{C}^{14} \].

For every element, while the atomic number remains consistent, the mass number can vary because the number of neutrons can change. This leads to what we call different isotopes of an element – each with a unique mass number. Knowing the mass number helps us understand not just the basic identity of isotopes but also facilitates calculations related to nuclear chemistry and physics.

Neutrons

Neutrons are neutral particles residing in the nucleus of an atom. They do not carry any electric charge but play a pivotal role in the stability and mass of the atom.

In the context of isotones, neutrons are critical. Isotones are defined as different elements (nuclides) that share the same number of neutrons. To find the number of neutrons in an atom, you would subtract the atomic number from the mass number:

• Number of neutrons = Mass number - Atomic number

For instance, potassium (K) with a mass number of 39 and an atomic number of 19, has 20 neutrons, calculated by \\[39 - 19 = 20\].

Neutrons contribute significantly to the atomic mass but not to the charge. They also play a role in determining which isotopes or isotones a particular element might form. As such, understanding the number of neutrons in elements is essential for grasping advanced concepts in nuclear and atomic physics.