Question

A 60.0-g sample of fermium-253 was placed in a sealed vessel 9.0 days ago. Only 7.5 g of this isotope is now left. What is the half-life of fermium-253?

Answer 1

The answer is 3.0 Days

Answer 2

Answer: 3.02 days

Explanation: This is a type of radioactive decay and all the radioactive process follow first order kinetics.

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

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

where,

k = rate constant

t = time taken for decay process

a = initial amount of the reactant

(a - x) = amount left after decay process

Putting values in above equation, we get:

`k=(2.303)/(9.0)\log(60.0g)/(7.5g)= 0.23days^(-1)`

To calculate the half life, we use the formula:

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

`t_(1/2)=(0.693)/(0.23)=3.02days`