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

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

$\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{105}=6.6\times 10^{-3}{\text {billion years^{-1}}$

$N=N_o\times e^{-\lambda t}$

N = amount left after time t  = ?

$N_0$ = initial amount = 240 g

$\lambda$ = rate constant  =$6.6\times 10^{-3}billion years^{-1}$

t= time  = 525 billion years

Putting in the values, we get

$N=240\times e^{- 6.6\times 10^{-3}billion years^{-1}\times 525 {\text {billion years}}$

$N=7.50g$

Answer 2

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