1.

It is observed that only 0.39% of the originalradioactive sample remains undecayed after eight hours. Select the correct options.

Answer»

The HALF-life of that SUBSTANCE is 1 hour.
The mean life of the substance is `1/(ln 2)` hour.
Decay constant of the substance is ln 2 per hour.
If the number of radioactive nuclei of thissubstance at a given instant is `10^8` then the numberleft after 30 min would be `sqrt2xx10^7`

Solution :Here, t=8 hours
As `N=N_0 e^(-lambdat)` [ Law of radioactive decay]
`rArr N/N_0=e^(-lambdat) rArr 0.0039 =e^(-lambda8)`
`rArr e^(8lambda)=1/0.0039 = 256` or `e^(8lambda)=2^8`
Taking natural logarithm on both sides , we get
`8 lambda = 8 ln2`
`lambda` = ln2 per hour
Again, half life `=T_(1//2)=(ln2)/lambda`=1 hour
Mean time, `tau =1/lambda=1/(ln2)` hour
`therefore N=(10)^8 (1/2)^(1//2)=1/sqrt2xx10^8`
or `N=5sqrt2xx10^7` .


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