A certain radioactive element disintegrates with a decay constant of `7.9 xx 10^(-10) //s` At a given instant of time, if the activity of the sample is equal to `55.3 xx 10^(11)` disintegration/second then number of nuclei at that instant of time ia

Options

A. `7.0 xx 10^(21)`
B. `4.27 xx 10^(13)`
C. `4.27 xx 10^(3)`
D. `6 xx 10^(23)`

Answer

a

Explanation

Decay constant `lambda = 7.9 xx 10^(-10)` /second
Activity, `A = 55.3 xx 10^(11) ("disintegration")/("second")`
Let the number of nuclei at that instant be N.
we know activity `A = lambda N`
`:. N = (A)/(lambda) = (55.3 xx 10^(11))/(7.9 xx 10^(-10)) = 7.0 xx 10^(21)`