Question

The half-life of Palladium-100 is 4 days. After 12 days a sample of Palladium-100 has been reduced to a mass of 4 mg. What was the initial mass (in mg) of the sample?

Answer 1

Answer : The initial mass of the sample is, 31.9 mg

Explanation :

Half-life = 4 days

First we have to calculate the rate constant, we use the formula :

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

$k=\frac{0.693}{4\text{ days}}$

$k=0.173\text{ days}^{-1}$

Now we have to calculate the initial mass of sample.

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

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

where,

k = rate constant  = $0.173\text{ days}^{-1}$

t = time passed by the sample  = 12 days

a = initial amount of the reactant  = ?

a - x = amount left after decay process = 4 mg

Now put all the given values in above equation, we get

$12=\frac{2.303}{0.173}\log\frac{a}{4}$

$a=31.9mg$

Therefore, the initial mass of the sample is, 31.9 mg