How many radioactive nuclei were present in the sample when it was shipped?

Question

A sample of the radioactive isotope Iodine-131 with an initial activity of 5 mCi is shipped to a medical lab. If this isotope has a half-life of 8.04 days, how many radioactive nuclei were present in the sample when it was shipped?

Answer 1

Well, just lemme know if the answer was correct or not :

A  = lambda * N ........ (1)

here,

lambda = decay constant

A = Activity

N = No. of nuclei

also, given A = 5 mCi = 5 * 10^-3 * 3.7 * 10^10 dps (disintegrations per second ) ........ ( 2)

now, lambda = 0.6931/ T  ( T = Half life)

so, lambda = 0.6931 / (8.04 * 24* 60* 60) { since activity is in /seconds so u have to convert T into seconds too} ........... (3)

solving (1 ) using (2) n (3) :

N = 1.854 * 10 ^ 14