Question 561: Atoms & Nuclei

Question

For a radioactive material, half-life is 10
minutes. If initially there are 600 number of
nuclei, the time taken (in minutes) for the
disintegration of 450 nuclei is

Accepted Answer

Given N
0
= 600, N
1
= 450, T = 10 min
Number of nuclei remaining, N = 600 Ã¢ÂÂ 450
= 150 after time Ã¢ÂÂtÃ¢ÂÂ
$${N \over {{N_0}}} = {{150} \over {600}} = {1 \over 4}$$
According to the law of radioactive decay,
N = N
0
e
-$$\lambda $$t
$${N \over {{N_0}}} = {\left( {{1 \over 2}} ight)^{{t \over {{T_{1/2}}}}}}$$
$$ 	herefore $$ $${{150} \over {600}} = {\left( {{1 \over 2}} ight)^{{t \over {{T_{1/2}}}}}}$$
$$ \Rightarrow $$ $${\left( {{1 \over 2}} ight)^2} = {\left( {{1 \over 2}} ight)^{{t \over {{T_{1/2}}}}}}$$
$$ \Rightarrow $$ t = 2T
1/2
= 2 $$ 	imes $$ 10 minutes = 20 minutes

Answer

20

Answer

10

Answer

30

Answer

15

Atoms & Nuclei

For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is

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