Question

The radioactive isotope ²³⁴Pa has a half-life of 6.70 h. A sample containing this isotope has an initial activity (t = 0) of 35.0µCi. Calculate the number of nuclei that decay in the time interval between t₁ = 7.0 h and t₂ = 14.0 h.
___________ Nuclei

Answer 1

Given that -

m = 35.0 uCi, Half-life, Hf = 6.70 h, t1=7.0 h, t2 = 14.0 h

Now, use the expression -

mr = mo/2^(t/hf)
at t1 mr = 35.0uCi/ 2^(7.0hr/6.7hr)
mr = 35.0/ 2^1.045
mr = 35.0/2.063
mr = 16.962 uCi remaining mass after t1

Again -

at t2 mr = 35.0/ 2^(14.0/6.7)
mr = 35.0/2^(2.089)
mr = 35.0/4.254
mr = 8.226 uCi remaining mass after t2

Therefore, the number of nuclei decayed ( n ) between t1 and t2 = mr after ti - mr after t2
= 16.962 uCi - 8.226 uCi
= 8.736 uCi