Question

If the half-life of 37Rb is 4.7x101 years, how long would it take for 0.5 grams of a 2 gram sample to radioactively decay?

Answer 1

Answer: The time required will be 19.18 years

Step-by-step explanation:

All the radioactive reactions follows first order kinetics.

The equation used to calculate half life for first order kinetics:

`k=(0.693)/(t_(1/2))`

We are given:

`t_(1/2)=4.7* 10^1yrs`

Putting values in above equation, we get:

`k=(0.693)/(4.7* 10^1yr)=0.015yr^(-1)`

Rate law expression for first order kinetics is given by the equation:

`k=(2.303)/(t)\log([A_o])/([A])`

where,

k = rate constant =
`0.015yr^(-1)`

t = time taken for decay process = ?

`[A_o]` = initial amount of the reactant = 2 g

[A] = amount left after decay process = (2 - 0.5) = 1.5 g

Putting values in above equation, we get:

`0.015yr^(-1)=(2.303)/(t)\log(2)/(1.5)\\\\t=19.18yrs`

Hence, the time required will be 19.18 years