A nucleus has a half-life of 30 minutes. At 3 PM its decay rate was measured as 120,000 counts/sec. What will be the decay rate at 5 PM ?

Options

A. 120,000 counts/sec
B. 60,000 counts/sec
C. 30,000 counts/sec
D. 75,00 counts/sec

Answer

D

Explanation

Given T= 30 minutes. `(dN)/(dt)`= 120K `("counts")/("sec")`
After each half life, activity is reduced to half therefore after n half lives activity reduces to `((1)/(2))^(n)`
Also `(dN)/(dt) prop N. (dN)/(dt)` at 5 P.M. will be equal to activity remaining after four half lives.
i.e., `((1)/(4))^(4)= ((1)/(16)th)` of the initial activity
`((dN)/(dt))_(" at 5 P.M") = ((1)/(16) th)` of the initial activity
`((dN)/(dt))_("5 P.M") = ((1)/(16)) ((dN)/(dt))_("3 PM")`
`rArr ((dN)/(dt))_("5 P.M") = 7500` counts/sec