Question

Mass number of a nucleus X is A and atomic number is Z. Find mass number and atomic number of the new nucleus (say Y) after the emission of m-alpha particles and n-beta particles.

Answer 1

Ans               Aeff=m(A-4) and zeff=m(Z-2)+n(Z+1)

Explanation:

                  in a alpha decay the atomic number decreases by 4 and is uneffected during beta decay

                   mass number is decreased by 2 during alpha decay and is increases  by1 during beta decay

Answer 2

After emissions of m Alpha particles Mass number of a nucleus X becomes A-4m & atomic number becomes Z-2m

After emissions of n Beta particles Mass number of a nucleus X remains A & atomic number becomes Z+n

1) Alpha decay

X (A , Z) ------> Y(A-4 , Z-2) + a ( 4 ,2)

+ energy

•where X is unstable nuclei

Y is daughter nuclei

a is alpha particle

•So, mass number of alpha particle is 4 and atomic No. is 2

• Therefore after emissions of m Alpha particles Mass number of a nucleus X becomes A-4m & atomic number becomes Z-2m i.e. the mass number & atomic No. of daughter nuclei.

2) Beta decay

X ( A , Z) ------> Y ( A , Z+1) + e ( 0 ,-1)

+ v + energy

•where X is unstable nuclei

Y is daughter nuclei

v is anti Neutrino particles ( for conservation of spin momentum)

• Therefore after emissions of n Beta particles Mass number of a nucleus X remains A & atomic number becomes Z+n i.e. the mass number & atomic No. of daughter nuclei.