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

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)

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 N0 (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

Posted by

Vakul

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