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?

Answers

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.

[tex]t_{\frac{1}{2}}=\frac{0.69}{k}[/tex]

[tex]k=\frac{0.69}{t_{\frac{1}{2}}}=\frac{0.693}{2hours}=0.346hours^{-1}[/tex]

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

[tex]A=A_0e^{-kt}[/tex]

where,

k = rate constant  

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

A = activity at time t = ?

[tex]A_0[/tex] = initial activity  = 600, 000

[tex]A=600000\times e^{-0.346\times 6}[/tex]

[tex]A=75258[/tex]

Thus there will be 75258 nuclei left at 6 pm.


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