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Question

The polonium isotope 21084Po is unstable, it emits an α - particle with energy 5.30 MeV. The atomic mass of 21084Po is 209.9829 u and atomic mass of 42He is 4.0026 u. Then,

A
Daughter nucleus is 20682Pb
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B
Disintegration energy of α - decay is 5.30 MeV
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C
Disintegration energy of α - decay is 5.40 MeV
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D
Mass of daughter nucleus is 205.9745 u
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Solution

The correct option is A Daughter nucleus is 20682Pb
By equation balancing we can write the chemical reaction as:
21084Po20682X+42+ΔQ
Clearly atom X is 20682Pb.

Now for disintegration energy:
By momentum conservation we can write that,
0=MlVlMαVα
MlMα=VαVl

Total energy of system after disintegration can be written as:
K.E.total=K.E.Pb+K.E.α
=12MlV2l+12MαV2α
=12(MαVα)Vl+12MαV2α
=K.E.α(1+VlVα)
=K.E.α(1+MαMl)
=K.E.α(Ml+MαMl)
=K.E.α(MPoMPoMα)
Putting respective values we get,
disintegration energy = 5.4 eV

ΔE=Δmc2
5.4 MeV=[MPoMPbMα]u×931.5 MeVu

Putting respective values, we can easily get value of mass of daughter nucleus as 205.9745u.




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