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Question

A radioactive sample has an initial activity of 28dpm 30 minutes later its activity 14dpm. How many atoms of nuclide were present initially?


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Solution

Step-1:Given data

  1. The initial activity of the radioactive sample is A1=28dpm.
  2. The final activity of the radioactive sample is A2=14dpm.
  3. The half time of the radioactive sample is T12=30min.

Step-2: The activity and half time of radioactive element

  1. The activity or decay rate is the number of decays per unit time and it is given by the form, A=λN, where, N is the number of radioactive nuclei present at a time, and λ is the decay constant.
  2. The half-life of a radioactive element is defined as, T12=0.693λ.

Step-3: Finding the initial activity

As we know, the half-life of a radioactive element isT12=0.693λ.

So,

λ=0.693T12=0.69330=0.231/min.orλ=0.231/min

Again, the initial activity of a radioactive element is A1=λNo, where No is the number of nuclei at the time t=0.

So,

No=A1λ=280.0231=1212orNo=1212

Therefore, the total number of nuclei present at the initial time is 1212.


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