Physics, asked by yeswadeep5659, 9 months ago

Half-life of a radioactive substance is T. At time t_1 activity of a radioactive substance is R_1 and at time t_2 it is R_2. Find the number of nuclei decayed in this interval of time.

Answers

Answered by RitaNarine
0

Given:

Half-life of a radioactive substance is T.

Activity of a radioactive substance, at T1 = R1

Activity of a radioactive substance, at T2 = R2

To Find:

the number of nuclei decayed in this interval of time.

Solution:

We know , decay constant ,

  • L = 0.693/T

Also, Number of nuclei at a time t , is

  • N = Noe^{-Lt}

Reactivity,

  • R = dN/dt =  - LNoe^{-Lt}

At t = T1, R = R1

and at t = T2 , R =R2

  • R1 = LNoe^{-LT1}  = - LN1
  • R2 = LNoe^{-LT2} = - LN2

Number of nuclei decayed = Number of nuclei left at t1 - Number of nuclei left at t2

  • Ndecay = N1 - N2 = - R1/L - - R2/L = (R2 - R1)T/0.693

The number of nuclei decayed in this interval of time is (R2 - R1)T/0.693.

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