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A radioactive nucleus A with a half life...

A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by :

A

`t=T/(log(1.3))`

B

`t = T/2 (log 2)/(log 1.3)`

C

t=T`(log 1.3)/(log 2)`

D

t = T log (1.3)

Text Solution

Verified by Experts

The correct Answer is:
C
`(N_(B))/(N_(A))=(N_(0)(1-e^(-lambdat)))/(N_(0)e^(-lambdat))`
`0.3 = e^(lambdat) -1 rArr T = ("In(2))/lambda`
`1.3 = e^(lambdat) -1 rArr T = ("In(2))/lambda `
`1.3 = e^(lambdat) rArr lambda = ("In(2)")/T `
In `(1.3) = lambdat`
` t = ("In"(1.3))/("In(2)") xxT`
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