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Question

An element X disintegrates by α-emission and the new element further disintegrates twice by β-emission and once by γ-emission. If Y is the final element formed, then:

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Solution

In an alpha emission, the atomic number of the parent nucleus decreases by 2, while the mass number decreases by 4. And in a beta emission, the atomic number of the parent nucleus increases by 1, while the mass number remains the same. There is no change in the atomic and mass numbers, in a gamma emission.
According to the given information, the element Y is formed from X as follows:

AZX α A4Z2X1

A4Z2X1 β A4Z2+1X2 = A4Z1X2

A4Z1X2 β A4Z1+1X3 = A4ZX3

A4ZX3 γ A4ZX3 = Y

Therefore, the atomic number of Y= atomic number of X=Z, but their mass numbers are different (A - 4A). So, X and Y are isotopes.

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