After 56 days, a 4.0-g sample of phosphorus-32 contains only 0.25 g of isotope. Based on this data,

what is the half-life of phosphorus-32?

324 hours (13.5 days)

Explanation:see attached photo

THE HALF LIFE OF PHOSPHORUS-32 ISOTOPE IS 14 DAYS.

Explanation:

Using the Nerst equation of half life;

t1/2 = t * in(2) / in (No/Nt)

where;

t1/2 = half life = the unknown

t = elapsed time = 56 days

No= initial mass of the sample = 4.0 g

Nt = final mass of the sample = 0.25 g

Substituting the values into the equation, we have;

t1/2 = 56 * Ln2  / Ln ( 4/0.25)

t1/2 = 56 * 0.6932 / Ln (16)      

t1/2 = 56 * 0.6932 / 2.7726      

t1/2 = 38.8192 / 2.7726

t1/2 = 14.001 days.

t1/2 = 14 days.

The half life of the phosphorus- 32 would be 14 days