Question

natural samarium has been found to emit alpha particle at a rate of 135 particles/gm/sec. the isotope Sm 147 (abundance 15 %) is responsible for the activity. what is its half life in years

Answer 1

1 mol of Sm will have 147g mass, right? {or is it 150?, it is 150 in my periodic table}

well, 15% of that is radioactive so you have **N** = 0.15 • A nuclei (A = avogadro) per mole

you know that the decay rate is 135parts/g/s, so that's **R** = 135 * 147 parts/sec/ mole.

equations:

t1/2 (half life) = ln(2)/lambda
AND lambda = R / N [you calculated R and N above]
this will be a huge number so convert seconds to years...

is that any help?