In the following nuclear reaction,
D→(α) D₁→(β -) D₂→(α) D₃→(γ) D₄
Mass number of D is 182 and atomic number is 74. Mass number and atomic number of D₄ respectively will be _________.

Solution

Physics sir · 3 steps

Track the mass number and atomic number together, one decay at a time, and do not let gamma fool you.

1. Decay rules. An α particle is ⁴₂He, so A drops by 4 and Z drops by 2. In β⁻ decay a neutron becomes a proton, so A stays the same and Z rises by 1. A γ ray is only energy, so neither A nor Z changes.

   Nucleus	Emission that formed it	Mass number A	Atomic number Z
   D	starting nucleus	182	74
   D₁	α	182 - 4 = 178	74 - 2 = 72
   D₂	β⁻	178	72 + 1 = 73
   D₃	α	178 - 4 = 174	73 - 2 = 71
   D₄	γ	174	71

2. Quick check. Two α decays remove 8 from A, giving 174. They remove 4 from Z, and the β⁻ adds 1 back, giving 74 - 4 + 1 = 71.
3. So. D₄ has mass number 174 and atomic number 71, which is option (a).

The idea to keep. Alpha: A - 4, Z - 2. Beta minus: A same, Z + 1. Gamma: no change at all. Count the alphas and betas, then add up the changes.

Answer from the NTA final answer key. Solution by PrepWiser.