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

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 = 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=(2.303)/(k)\log(1.0)/(0.2)`

`k=(2.303)/(6)\log(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_{(1)/(2)}=(0.693)/(k)`

`t_{(1)/(2)}=(0.693)/(0.268)=2.58days`

The half life is 2.58 days