Question

A radioactive source is prepared by chemically separating 90 Sr from other elements. Initially, the source contains only 90 Sr but this radionuclide decays to a radioactive daughter 90 Y, which, after some time, reaches secular equilibrium with its parent. What is the time after the source is created that the activity of the daughter 90 Y is within 5% of that of the parent? I got 277 hours, is this correct?

Explain whether the following statement is true or false

"Gamma rays are not directly ionizing radiation because their interaction with matter produces no charged particles"

Answer 1

given radioactive sample 90 Sr and 90 Y
half life of 90 Sr = t" = 28.8 years = 183340.8 hours
half life of 90 Y = t' = 64.1 hours

now, initial number of atoms of 90 Sr = No
after time t
number of atoms of 90 Sr = No - N
number of atoms of 90 Y = N - N'
but
N = No*e^(-t*ln(2)/t")
N' = N*e^(-t*ln(2)/t')

hence
form the question
activity of 90Y is within 0.95 of activity of 90 Sr

at time t
activity of 90Sr = d(No - N)/dt = -dN/dt = ln(2)Noe^(-t*ln(2)/t")/t"
activity of 90Y = d(N - N')/dt = dN/dt - dN'/dt = ln(2)Ne^(-t*ln(2)/t')/t' + ln(2)No*e^(-t*ln(2)/t")/t" -ln(2)Noe^(-t*ln(2)/t")/t" = ln(2)N*e^(-t*ln(2)/t')/t'
hence
from the given data
ln(2)N*e^(-t*ln(2)/t')/t' = 0.95*ln(2)Noe^(-t*ln(2)/t")/t"
3010.7693 = e^(-t*ln(2)/t" + t*ln(2)/t" + t*ln(2)/t')
8.0099509 = ln(2)(t(1/t' + 1/t" - 1/t"))
8.0099509 = ln(2)(t(1/t'))
t = 740.734246 hours = 30.8639 days

hence in 30.86 days the daughter nuclei will have activity within 95% of the parent nuclei

Gamma rays are actually inonising radiation as they can knock off electrons from the orbitals of atoms leaving positive ion