Cesium-137, used in cancer treatment, has a half-life of 30 years.

Question

Enter the balanced nuclear equation for the beta decay (0/-1e) of cesium-137.

How many milligrams of a 36 mg sample of celsium 137 remain after 120 years

Express the mass to two significant figures and include the appropriate units.

How many years are required for 26mg  of cesium-137 to decay to 13  mg of cesium-137?

Express the time in years to two significant figures.

Answer 1

¹³⁷₅₅Cs→¹³⁷₅₆Ba + ⁰_-1β

For first order decay, you can use the following formula:

Fraction Remaining (FR) = 0.5ⁿ where n = number of half lives that have elapsed

t1/2 = 30 yrs

120 yrs x 1 half life/30 yrs = 4 half lives have elapsed; n = 4

FR = 0.5⁴

FR = 0.0625

If you start with 36 mg and 0.0625 remains, that would be

36 mg x 0.0625 = 2.25 mg = 2.3 mg (2 sig. figs.)