The element with atomic number $84$ and mass number $218$ changes to another element with atomic number $84$ and mass number $214$. The number of alpha and beta-particles emitted are respectively
A. $1,3$
B. $1,4$
C. $1,2$
D. $1,5$

Hint:This concept comes from nuclear chemistry, when a heavier particle breaks down itself into lighter particles than this concept can be termed as Nuclear fusion, on the other hand when two lighter elements combine together to form a heavier particle is called nuclear fission.

Complete step-by-step solution:
Let us start the question! On fusion or fission some particles decay into radioactive species. There can be different radioactive decay that can be alpha, beta and gamma. Alpha particles carry a positive charge, beta particles carry a negative charge, and gamma rays are neutral. An alpha particle is made up of two protons and two neutrons bound together. Beta particles are high energy electrons. Gamma rays are waves of electromagnetic energy, or photons. In the question it is asked to tell the number of alpha and beta particles emitted when an element having atomic number $84$ changes to another element having atomic number $84$ and mass number from $218$ to $214$. We can calculate by using the formula.
\[^{218}{X_{84}}{ \to ^{214}}{X_{84}}{ + _{x + 2}}{\alpha ^4}{ + _{y - 1}}{\beta ^0}\]
To calculate number of alpha particles: Difference between the mass numbers divided by four.
Number of alpha particle is
\[ = \dfrac{{218 - 214}}{4} = \dfrac{4}{4} = 1\]
Number of beta particle is
\[ = 84 - 84 + 2 \times 1 = 2\]
Option C) is the correct option for this question. Number of alpha particles emitted is $1$ and the number of beta particles emitted is $2$.

Note:We need to know that an alpha particle is made up of two protons and two neutrons bound together. Beta particles are high energy electrons. Gamma rays are waves of electromagnetic energy, or photons. Alpha decay occurs because the nucleus of a radioisotope has too many protons. A nucleus with too many protons causes repulsion between these charges.