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A radioactive substance X decays into an...

A radioactive substance X decays into another radioactive substance Y Initially only X was present. `lambda_(x)` and `lambday_(y)` are the disnttegration constants of Xa nd Y `N_(x)` and `N_(y)` are the number of nuclie of X and Y at any time t. Number of nuclei `N_(y)` will be maximum when

A

`(N_(Y))/(N_(X)-N_(Y))=(lamda_(Y))/(lamda_(X)-lamda_(Y))`

B

`(N_(X))/(N_(X)-N_(Y))=((lamda_(Y))/(lamda_(X))-lamda_(Y))^(2)`

C

`lamda_(Y)N_(Y)=lamda_(X)N_(X)`

D

`lamda_(Y)N_(X)=lamda_(X)N_(Y)`

Text Solution

Verified by Experts

The correct Answer is:
C
At any instant
`(dN_(y))/(dt)=lamda_(x)N_(x)-lamda_(y)N_(y)`
For maximum `N_(y),(dN_(y))/(dt)=0`
`:.lamda_(x)N_(x)=lamda_(y)N_(y)`
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