What is the number of grams and the half life?

Question

Strontium 90 is a radioactive isotope that decays exponentially at 2.8% per year. Suppose there are initially 1000 grams of strontium 90 in a substance.

if the decay uses the formula P=P₀e^rt

show solutions:

a.Determine the number of grams of strontium 90 left after 50 years

b.determine the half-life of strontium 90

Answer 1

P(t) = P₀e^rt

1. P(t) = amount of strontium left after t years
2. P0= initial amount of strontium = 100 grams
3. r = decay rate expressed as a decimal = -2.8% = -0.28
4. t = years

a) P = 100·e^(-0.28)(50) Use your calculator to get the answer

b) Half-life means the number of years for the strontium to decay to one half (50 grams) of its starting value.

P = P₀e^rt

50 = 100e^-0.028t

(1/2) = e^-0.028t

ln(1/2) = -0.028 t

Solve for t. Use your calculator to compute the answer. Round to the nearest year.