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

Answer 1

The disintegration of 450 nuclei is 20

Answer 2

Answer : 20 minutes

Explanation: the half life is given as 10 minutes

Initial number of nuclei = 600 = N1

Final number of nuclei : 450

To find:

Time required for disintegration of 450 nuclei (in minutes)

N= (final number of nuclei - initial number if nuclei)

= 600-450

= 150

N/N1= (1/2) ^t/TH

150/600 = (1/2) ^t/10

1/4 = (1/2) ^t/10

(1/2)^2 = (1/2) ^t/10

Therefore

2=t/10

Since the bases are same, we're equating the powers

Therefore

t= 20 mins

Half-life t1⁄2) is defined as the time required for a quantity to reduce to half of its initial value.