Question

74Be decays with a half-life of about 53 d. It is produced in the upper atmosphere, and filters down onto the Earth's surface.

If a plant leaf is detected to have 350 decays/s of 74Be, how long do we have to wait for the decay rate to drop to 25 per second?

Answer 1

201.8 days

Step-by-step explanation:

The activity of a radioactive sample as a function of times is :

`$R=R_0e^{(0.693t)/(T_(1/2))}$`

Here,
`$R_0$` = the initial activity

`$T_(1/2)$` = half life

t = elapsed time

Now rearranging the equation for time, t, we get:

`$(R)/(R_0)=e^{-(0.693t)/(T_(1/2))}$`

`$\ln\left((R)/(R_0)\right)=-(0.693t)/(T_(1/2))$`

`$t=(-\ln\left((R)/(R_0)\right)T_(1/2))/(0.693)$`

`$t=(-\ln\left((25)/(350)\right)* 53)/(0.693)$`

= 201.8 days

Therefore, the required time is 201.8 days