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

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:

$k=\frac{2.303}{t}\log\frac{a}{a-x}$

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:

$k=\frac{2.303}{9.0}\log\frac{60.0g}{7.5g}= 0.23days^{-1}$

To calculate the half life, we use the formula:

$t_{1/2}=\frac{0.693}{k}$

$t_{1/2}=\frac{0.693}{0.23}=3.02days$

Answer 2

The answer is 3.0 Days