Question

You find a bag labeled "10 kg of lead-210". Its contents now weigh 1.25 kg. How many half-life periods have there been since the bag was weighed and labeled? Lead-210 is a radioisotope with a half-life of about 22 years.

Answer 1

Answer : The number of half-life periods will be, 3

Explanation :  Given,

Initial amount of lead = 10 kg

Amount of lead after decay = 1.25 kg

Half-life = 22 years

Formula used :

$a=\frac{a_o}{2^n}$

where,

a = amount of reactant left after n-half lives

$a_o$ = Initial amount of the reactant

n = number of half lives

$t_{1/2}$ = half-life

Now put all the given values in the above formula, we get:

$1.25=\frac{10}{2^n}$

$2^n=8$

$2^n=2^3$

$n=3$

Thus, the number of half-life periods will be, 3