Question

The half-life of the radioisotope 158Eu is 0.77 h. How much time is required for a 160.0-g sample of 158Eu to decay to 2.07 g?

a. 3.0 h
b. 4.0 h
c. 6.0 h
d. 2.1 h
e. 4.8 h

Answer 1

Answer: e. 4.8 h

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 = let initial amount of the reactant

a - x = amount left after decay process

a) for rate constant

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)/(0.77hr)=0.9hr^(-1)`

b) for 160.0 g to decay to 2.07 g

`t=(2.303)/(0.9)\log(160.0)/(2.07)`

`t=4.8hr`

The time required for a 160.0-g sample of 158Eu to decay to 2.07 g is 4.8 hours