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Question
An element P disintegrates by α-emission and the new element suffers two further disintegration, both by β-emission, to form an element Q. Explain that fact P and Q are isotopes.
Solution
Let mass number of P = A
Let atomic number of P = Z
Nuclear reaction for α-emission
\[\ce{^A_zP -> ^{A-4}_{Z-1}X + ^4_2He}\](α- particles)
Nuclear reactions foe two further β-emission
\[\ce{^{A-4}_{Z-2}X-> ^{A-4}_{Z-4}Y + ^0_-1e}\] (β-emission)
\[\ce{^{A-4}_{Z-1}Y-> ^{A-4}_ZQ + ^0_-1e}\] (β-emission)
The atomic numbers (Z) of P and Q are the same but their mass numbers [A and (A-4)] are different. So P and Q are isotopes.
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