Question

You have just isolated a new radioactive element. If you can determine its half-life, you will win the Nobel Prize in physics. You purify a sample of 2 grams. One of your colleagues steals half of it, and six days later you find that 0.2 gram of the radioactive material is still left. What is the half-life

Answer 1

Answer: 2.58 days

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  = 6 days

a = initial amount of the reactant  =  1 g

a - x = amount left after decay process   = 0.2 g

a) to find the rate constant

$6=\frac{2.303}{k}\log\frac{1.0}{0.2}$

$k=\frac{2.303}{6}\log\frac{1.0}{0.2}$

$k=0.268days^{-1}$

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.

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

$t_{\frac{1}{2}}=\frac{0.693}{0.268}=2.58days$

The half life is 2.58 days