The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive
substance is

  • Option 1)

    15

  • Option 2)

     

    30

  • Option 3)

    45

  • Option 4)

    60

 

Answers (1)
V Vakul

As discussed

Number of nuclei after disintegration -

N=N_{0}e^{-lambda t} or A=A_{0}e^{-lambda t}

- wherein

Number of nucleor activity at a time is exponentional function

 

 Let's say it decays 40% after time t1 and 85% decay after time t2 . Then at t=t1 , N1 = 0.6 N(N0 = initial number of nuclei)

at t = t2, N2 = 0.15 N0

N_{1} = 0.60 N_{0} = N_{0}. \:e^{-\lambda t_{1}}  -1

N_{2} = 0.15 N_{0} = N_{0}. \:e^{-\lambda t_{2}}  -2

Divide 2 into 1

4 = e^{\lambda \left ( t_{2}-t_{1} \right )}

or t_{2} - t_{1} = 2 \frac{ln^{2}}{\lambda } = 2\:t_{\frac{1}{2}}

                    = 60 minutes


Option 1)

15

This option is incorrect

Option 2)

 

30

This option is incorrect

Option 3)

45

This option is incorrect

Option 4)

60

This option is correct

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