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in Physics by (45.1k points)

A radionuclide X is produced at constant rate α. At time t = 0, number of nuclei of X are zero. Find

(a) the maximum number of nuclei of X.

(b) the number of nuclei at time t.

Decay constant of X is λ.

1 Answer

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Best answer

(a) Let N be the number of nuclei of X at time t.

Rate of formation of X = α

Rate of disintegration = λN

Number of nuclei of X will increase until both the rates will become equal. 

Therefore,

(b) Net rate of formation of X at time t is,

Integrating with proper limits, we have

This expression shows that number of nuclei of X are increasing exponentially from 0 to α/λ.

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