Question

A 100 gram sample of Cerium-143 has a half life of 33 hours. How Long will it take until there are only 6.25 grams of cerium-143 left?

Answer 1

Q.
a 100 - gram sample of cerium-143 has a half life of 33 hours. how long will it take until there are only 6.25 grams of cerium-143 left?


answer 132 hours

Answer 2

Answer: The time taken by Cerium-143 will be 132.051 hours.

Step-by-step explanation:

All the decay processes follow first order kinetics.

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

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

where,

`t_(1/2)` = half life of the reaction = 33 hours

k = ?

Putting values in above equation, we get:

`k=(0.693)/(33hrs)=0.021hrs^(-1)`

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

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

where,

k = rate constant =
`0.021hrs^(-1)`

t = time taken for decay process = ? hours

a = initial amount of the reactant = 100 grams

a - x = amount left after decay process = 6.25 grams

Putting values in above equation, we get:

`t=(2.303)/(0.021hrs^(-1))\log(100g)/(6.25g)\\\\t=132.051hours`

Hence, the time taken by Cerium-143 will be 132.051 hours.