Question

Nucleus A is converted into C through the following reactions:
$A⟶B+\alpha [\alpha -alphaparticle;\beta -electron]B⟶C+2\beta$
Then:

• A. A and B are isotopes
• B. A and C are isobars
• C. A and B are isobars
• D. A and C are isotopes

Answer 1

The correct option is D A and C are isotopes

Concept : αα decay decreases the mass number of the nucleus by $4$ and decreases atomic number of nucleus by $2$.

ββ decay increases the atomic number by $1$ whereas the mass number remains the same.

Let the nucleus $A$ be as ${}_Z^{A}A$.

Thus after $\alpha$ decay, the nucleus B will be as ${}_{Z-2}^{A-4}B$.

Then after $2$ $\beta$ decays, the nucleus C will be ${}_Z^{A-2}C$

$⟹$ A and C are isotopes as these have same atomic number but different mass numbers.