Plutonium-241 has a half-life of 14 years. If one has a sample of 160 g of plutonium-241, determine the mass of plutonium-241 that remains after 70 years.

Question

i would like to see work being shown

Answer 1

Adams,

 

Please take a look at solutions to similar problems that you posted at

 

https://www.wyzant.com/resources/answers/254587/a_sample_initially_contains_80_0_grams_of_thorium_234_after_48_days_only_10_grams_of_thorium_remains_determine_the_half_life_of_thorium_234

 

and at

 

https://www.wyzant.com/resources/answers/254581/the_half_life_of_francium_212_is_19_minutes_how_do_i_determine_the_number_of_minutes_it_takes_for_8_0_grams_of_this_isotope_to_decay_to_0_250_grams

 

The solutions entail the same methods.

 

Solution to latest problem:

 

T_1/2 = 14 years

 

Use the formula 

 

k = -ln(1/2) / T_1/2 = [-ln(0.5) / 14] years^-1 = 0.04951 years^-1

 

m(t) = m(0)e^-kt = m(0)e^-0.04951t , t in years

 

m(70) = 160e^-0.04951*70 = 5.00 grams

 

There are 5.00 grams left after 70 years.