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The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an
A
Isotope of parent
B
Isobar of parent
C
Isomer of parent
D
Isotone of parent
Detailed Solution
Let the parent be $^A_ZX$ and let it emit n alpha particles and 2n beta particles.
Each alpha emission reduces Z by 2 and A by 4: after n alpha particles, Z becomes Z − 2n and A becomes A − 4n.
Each beta emission increases Z by 1 and leaves A unchanged: after 2n beta particles, Z becomes Z − 2n + 2n = Z.
The daughter is $^{A-4n}_ZY$: it has the same atomic number as the parent but a different mass number.
Atoms with the same Z and different A are isotopes.
Hence the daughter is an isotope of the parent.
Each alpha emission reduces Z by 2 and A by 4: after n alpha particles, Z becomes Z − 2n and A becomes A − 4n.
Each beta emission increases Z by 1 and leaves A unchanged: after 2n beta particles, Z becomes Z − 2n + 2n = Z.
The daughter is $^{A-4n}_ZY$: it has the same atomic number as the parent but a different mass number.
Atoms with the same Z and different A are isotopes.
Hence the daughter is an isotope of the parent.