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A radioactive atom ' \( X^{\prime} \) emits a \( \beta- \) particle to produce an atom ' \( Y \) ' which then emits an \( \alpha \) -particle to given an \( \operatorname{atom}^{\prime} Z^{\prime}: \) (1) The atomic number of ' \( X^{\prime} \) is less than that of \( ^{\prime} Z^{\prime} \) (2) The atomic number of ' \( Y \) ' is less than that of \( ^{\prime} Z^{\prime} \) (3) The mass number of ' \( X^{\prime} \) is same as that of ' \( Y \)

1. 1,2 and 3 are correct
2. 1 and 2 are correct
3. 2 and 3 are correct
4. 3 is correct

Correct answer: 3 is correct

Solution

A beta-minus decay increases atomic number by 1 while leaving mass number unchanged, so X and Y have the same mass number. Then an alpha decay decreases atomic number by 2 and mass number by 4, making Z have atomic number one less than X and mass number four less than Y. Thus only statement 3 is true.

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