You have 42,784 grams of a radioactive kind of curium. If its half-life is 18 years, how much will be left after 72 years?

2,674.14 g

Step-by-step explanation:

Recall that the formula for radioactive decay is

N = N₀ e^ (-λt)

where,

N is the amount left at time t

N₀ is the initial amount when t=0, (given as 42,784 g)

λ = coefficient of radioactive decay

= 0.693 : Half Life

= 0.693 : 18

= 0.0385

t = time elapsed (given as 72 years)

e = exponential constant (approx 2.7183)

If we substitute these into our equation:

N = N₀ e^ (-λt)

= (42,787) (2.7183) ^[ (-0.0385) (72) ]

= (42,787) (2.7183) ^ (-2.7726)

= (42,787) (0.0625)

= 2,674.14 g