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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:

A
X and Y are isotopes.
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B
X and Y are isobars.
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C
X and Y are isotones.
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D
None of the above
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Solution

The correct option is A X and Y are isotopes.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→ A−4Z−2X1 A−4Z−2X1 β→ A−4Z−2+1X2 = A−4Z−1X2 A−4Z−1X2 β→ A−4Z−1+1X∗3 = A−4ZX∗3 A−4ZX∗3 γ→ A−4ZX3 = Y Therefore, the atomic number of Y= atomic number of X=Z, but their mass numbers are different (A - 4≠A). So, X and Y are isotopes.

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