Question

A certain radioactive element has a half life of 8694 years. How much of a 8.30 g sample is left after 8323 years

Answer 1

Answer: The amount of sample left after 8323 years is 4.32g

Step-by-step explanation:

Expression for rate law for first order kinetics is given by:

`t=(2.303)/(k)\log(a)/(a-x)`

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process

a) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

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

`k=(0.693)/(8694years)=7.97* 10^(-5)years^(-1)`

b) amount left after 8323 years

`t=(2.303)/(7.97* 10^(-5))\log(8.30g)/(a-x)`

`8323=(2.303)/(7.97* 10^(-5))\log(8.30g)/(a-x)`

`0.285=\log(8.30)/(a-x)`

`(8.30)/(a-x)=1.92`

`(a-x)=4.32g`

The amount of sample left after 8323 years is 4.32g