Question

A radioactive isotope has a half-life of 2 hours. If a sample of the element contains 600,000 radioactive nuclei at 12 noon, how many radioactive nuclei would be left at 6 pm?

Answer 1

Answer: There will be 75258 nuclei left at 6 pm.

Explanation:

a) half-life of the radioactive substance:

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

$t_{\frac{1}{2}}=\frac{0.69}{k}$

$k=\frac{0.69}{t_{\frac{1}{2}}}=\frac{0.693}{2hours}=0.346hours^{-1}$

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

$A=A_0e^{-kt}$

where,

k = rate constant  

t = time for decomposition = 6 hours ( from 12 noon to 6 pm)

A = activity at time t = ?

$A_0$ = initial activity  = 600, 000

$A=600000\times e^{-0.346\times 6}$

$A=75258$

Thus there will be 75258 nuclei left at 6 pm.