Question

The number of radioactive nuclides from a radioactive source has reduced to 1/6

from its original value in 60 seconds. Find the decay constant for this source.​

Answer 1

λ = 0.03 s⁻¹

Step-by-step explanation:

The formula for decay constant can be used as follows:

`N = N_oe^(-\lambda t)\\\\(N)/(N_o) = e^(-\lambda t)`

where,

`(N)/(N_o)` = ratio of remaining nuclei to the initial value of nuclei =
`(1)/(6)` = 0.167

t = time = 60 s

λ = decay constant = ?

Therefore,

`0.167 = e^(-\lambda(60\ s))\\\\-\lambda (60\ s) = ln(0.167)\\\\\lambda = (-1.7917)/(- 60\ s)`

λ = 0.03 s⁻¹