Question

If a sample of radioactive isotopes takes 600 minutes to decay from 400 grams to 50 grams, what is the half-life of the isotope?

Answer 1

Answer:

200 minutes

Explanation:

Answer 2

Answer : The half-life of the radioactive isotope is, 200 min.

Solution :

As we know that the radioactive isotopes decays follow first order kinetics.

So, the 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  = 600 min

a = initial amount of the reactant  = 400 g

a - x = amount left after decay process  = 50 g

Now put the all given values in above equation, we get the value of rate constant.

$k=\frac{2.303}{600}\log\frac{400}{50}=3.466\times 10^{-3}min^{-1}$

Now we have to calculate the half life of a radioisotope.

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

Putting value of 'k' in this formula, we get the half life.

$t_{1/2}=\frac{0.693}{3.466\times 10^{-3}min^{-1}}=199.94min=200min$

Therefore, the half-life of a radioactive isotope is, 200 min.