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NEET PHYSICSEasy

The decay constant of a radio isotope is λ\lambda. If A1A_1 and A2A_2 are its activities at times t1t_1 and t2t_2 respectively, the number of nuclei which have decayed during the time (t1−t2)(t_1 - t_2) is:

A

A1t1−A2t2A_1 t_1 - A_2 t_2

B

A1−A2A_1 - A_2

C

(A1−A2)/λ(A_1 - A_2) / \lambda

D

λ(A1−A2)\lambda (A_1 - A_2)

Step-by-Step Solution

  1. Definition of Activity: The activity (AA) of a radioactive substance is defined as the rate of disintegration of nuclei. It is related to the number of undecayed nuclei (NN) present at that instant and the decay constant (λ\lambda) by the relation: A=λNA = \lambda N .
  2. Relate N to A: From the relation, we can express the number of nuclei as N=AλN = \frac{A}{\lambda}.
  3. Initial and Final States:
  • At time t1t_1, activity is A1A_1, so the number of nuclei present is N1=A1λN_1 = \frac{A_1}{\lambda}.
  • At time t2t_2, activity is A2A_2, so the number of nuclei present is N2=A2λN_2 = \frac{A_2}{\lambda}.
  1. Calculate Decayed Nuclei: The number of nuclei that have decayed during the interval is the difference between the initial number of nuclei and the final number of nuclei. Number decayed=N1−N2\text{Number decayed} = N_1 - N_2 Number decayed=A1λ−A2λ=A1−A2λ\text{Number decayed} = \frac{A_1}{\lambda} - \frac{A_2}{\lambda} = \frac{A_1 - A_2}{\lambda}
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