Question

If we start with 1.000 g of strontium-90, 0.908 g will remain after 4.00 yr This means that half-life of strontium-90 is _________ yr.

A) 3.05

B) 4.40

C) 28.8

D) 3.63

E) 41.6

Answer 1

Answer: C) 28.8

Step-by-step explanation:

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

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

where,

k = rate constant

t = age of sample

a = initial amount of the reactant = 1.000 g

a - x = amount left after decay process = 0.908 g

a) to find rate constant

`4.00yr=(2.303)/(k)\log(a)/(a-x)`

`k=(2.303)/(4.00)\log(1.000)/(0.908)`

`k=0.024yr^(-1)`

b) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

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

`k=(0.693)/(0.024yr^(-1))=28.8yr`

The half-life of strontium-90 is 28.8 yr.