Question

Which of the following are isotopes?
(i) Atom, whose nucleus contains $ 20p+15n $ .
(ii) Atom, whose nucleus contains $ 20p+17n $ .
(iii) Atom, whose nucleus contains $ 18p+22n $ .
(iv) Atom, whose nucleus contains $ 18p+21n $ .
1) (i) and (iii)
2) (i) and (ii)
3) (ii) and (iii)
4) (iii) and (iv)

Answer 1

Hint: Two or more forms of elements which consist of the same number of protons but differ in number of neutrons in their nuclei, and hence, differ in their mass number are known as isotopes. Due to the same number of electrons and protons, the chemical and physical properties of isotopes are similar.

Complete answer:
Mass number: We know that the mass of an atom is concentrated at the centre i.e., nucleus which consist of protons and neutrons. Hence the mass number for an element is the summation of the number of protons and the number of neutrons present in the nucleus. It is represented by the symbol ‘A’. Both protons and neutrons in the nucleus are known as nucleons. As the mass of electrons is negligible, so the atomic mass of an element is equal to its mass number.
Mathematically it is represented as follows:
 $ A=p+n $
Where, $ p $ is the number of protons and $ n $ is the number of neutrons.
Atomic number: It is defined as the total number of protons present in the nucleus of an atom. It is represented by the symbol ‘Z’. Mathematically, it is represented as follows:
 $ Z=p=e $
Where, $ p $ is the number of protons and $ e $ is the number of electrons in an atom.
If two or more forms of elements consist of different mass numbers but same atomic number, are known as isotopes.
For given options, the mass number and atomic number for each atom is calculated as follows:
(i) Atom, whose nucleus contains $ 20p+15n $ .
Mass number $ A=20+15\Rightarrow 35 $
Atomic number $ Z=20 $
(ii) Atom, whose nucleus contains $ 20p+17n $ .
Mass number $ A=20+17\Rightarrow 37 $
Atomic number $ Z=20 $
(iii) Atom, whose nucleus contains $ 18p+22n $ .
Mass number $ A=18+22\Rightarrow 40 $
Atomic number $ Z=18 $
(iv) Atom, whose nucleus contains $ 18p+21n $ .
Mass number $ A=18+21\Rightarrow 39 $
Atomic number $ Z=18 $
As, pairs (i), (ii) and (iii), (iv) have different mass numbers but same atomic numbers. So, these represent the pairs of isotopes.
Hence, options (2) and (4) are correct.

Note:
Generally it is observed that different isotopes of the same element undergo the same reaction with different reaction rates. This is because different mass numbers lead to different activation energies and hence change in rate of reactions is observed. This is known as the kinetic isotopic effect.