Question

Lanthanum-138 has a half-life of 105 billion years. After 525 billion years, how much of a 240 g sample of this radioisotope will remain?

nevermind, I got 7.5g and was right

Answer 1

I got 7.5g aswell, and it was right aswell.

Answer 2

Answer: 7.50 grams of radioactive isotope will remain

Explanation:- Radioactive decay follows first order kinetics

Half-life of sample of lanthanum-138 = 105 billion years

`\lambda =\frac{0.693}{t_{(1)/(2)}}=(0.693)/(105)=6.6* 10^(-3){\text {billion years^(-1)}`

`N=N_o* e^(-\lambda t)`

N = amount left after time t = ?

`N_0` = initial amount = 240 g

`\lambda` = rate constant =
`6.6* 10^(-3)billion years^(-1)`

t= time = 525 billion years

Putting in the values, we get

`N=240* e^{- 6.6* 10^(-3)billion years^(-1)* 525 {\text {billion years}}`

`N=7.50g`