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A parent nucleus X undergoes alpha-under...

A parent nucleus X undergoes `alpha`-undergoes `alpha`-decay with a half-life of 75000 years. The daughter nucleus Y undergoes `beta`-decay with a half-life of 9 months. In a particular sample, it is found that the rate of emission of `beta`-particles is nearly constant (over several months) at `10^(7)//"hour"`. What will be the number of `alpha`-particles emitted in an hour ?

A

`10^(2)`

B

`10^(7)`

C

`10^(12)`

D

`10^(14)`

Text Solution

Verified by Experts

The correct Answer is:
B
As we know that radioactive decay is a spontaneous process. So, emission of alpha and beta particles can occur simultaneously.
`therefore` From the law of radioactive decay,
`(-(dN)/(dt))_(alpha-"particle") = lambda_(alpha) N_(alpha) and (-(dN)/(dt))_(beta-"particle") = lambda_(beta) N_(beta)`
Now, `lambda_(alpha)N_(alpha) = lambda_(beta) N_(beta)` (At steady state)
`rArr" "(-(dN)/(dt))_(alpha-"particle") = (-(dN)/(dt))_(beta-"particle")`
`rArr" "(-(dN)/(dt))_(alpha-"particle") = 10^(7)//"hour"`
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