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

Explanation:

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  

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.

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

$k=\frac{0.693}{0.77hr}=0.9hr^{-1}$

b) for 160.0 g to decay to 2.07 g

$t=\frac{2.303}{0.9}\log\frac{160.0}{2.07}$

$t=4.8hr$

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