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The elements with atomic number $ 84 $ and mass number $ 218 $ change to other elements with atomic number $ 84 $ and mass number $ 214 $ . The number of $ \alpha - $ and $ \beta - $ particle emitted respectively:
 $ A)1,3 \\
  B)1,4 \\
  C)1,2 \\
  d)1,5 $

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Answer
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Hint : 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.

Complete Step By Step Answer:
 $ _{84}{X^{218}}{ \to _{84}}{Y^{214}} + {X_{ + 2}}{\alpha ^4} + {Y_{ - 1}}{\beta ^0} $
Alpha particles consist of two protons and two neutrons bound together into a particle identical to a nucleus. They are generally produced in the process of alpha decay, but may also be produced in other ways.
Number of $ \alpha - $ particles $ = \dfrac{{218 - 214}}{4} $
 $ = \dfrac{4}{4} = 1 $
A beta particle, also called beta ray or beta radiation, is a high-energy, high-speed electron or positron emitted by the radioactive decay of an atomic nucleus during the process of beta decay. There are two forms of beta decay, $ {\beta ^ - } $ decay and $ {\beta ^ + } $ decay, which produce electrons and positrons respectively.
Number of $ \beta - $ particles $ = 84 - 84 + 2 \times 1 $
 $ = 2 $ .
So the correct answer is $ C)1,2 $ .

Additional Information:
Alpha particles can travel in vacuum Because of their charge and large mass, alpha particles are easily absorbed by materials, and they can travel only a few centimeters in air. They can be absorbed by tissue paper or by the outer layers of human skin.

Note :
Radioactive particles that radiate alpha and beta particles are most destructive when gulped, breathed in, retained, or infused. Gamma beams are the most hurtful outer danger. Beta particles can mostly enter skin, causing beta consumption. Alpha particles can't infiltrate flawless skin.