PLEASE HELP: What mass of phosphorus-32, in milligrams, is left from an original sample of 175 mg of Na₃³²PO₄ after 58.6 days?

Question

Phosphorus-32 is a commonly used radioactive nuclide in biochemical research, particularly in studies of nucleic acids. The half-life of phosphorus-32 is 14.3 days. What mass of phosphorus-32, in milligrams, is left from an original sample of 175 mg of Na₃³²PO₄ after 58.6 days? Assume that the atomic mass of ³²P is 32.0.

Answer 1

Radioactive decay is first order. There are a couple of formula that can be used but I find the following the easiest:

FR = 0.5ⁿ

FR = fraction remaining = ?

n = the number of half lives that have elapsed = 58.6 days x 1 half life / 14.3 days = 4.098 half lives elapsed

Solving fo FR we have..

FR = 05^4.098

FR = 0.0584

Since this is the fraction that remains, to find the mass (mg) that remains, we multiply this by the original mass

of ³²P. In this problem, we first have to find out how much of the 175 mg of Na₃³²PO₄ is ³²P.

molar mass Na₃PO₄ = 164 g / mol

atomic mass P = 32.0 g / mol

%P = 32.0 / 164 (x100) = 19.5%

mass of P in 175 mg of Na₃PO₄ = 0.195 x 175 mg = 34.1 mg of P

Mass of ³²P remaining = 0.0584 x 34.1 mg = 1.99 mg ³²P remaining