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.

Step-by-step 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_{(1)/(2)}=(0.69)/(k)`

`k=\frac{0.69}{t_{(1)/(2)}}=(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* e^(-0.346* 6)`

`A=75258`

Thus there will be 75258 nuclei left at 6 pm.