Question

Potassium-40 has a half-life of 1.277 x 109 years. After 1.022 x 1010 years, how much potassium-40 will remain from a 500.3-g sample?
A. approximately 1.95 g
B. approximately 3.91 g
C. approximately 62.54 g
D. approximately 71.47 g

Answer 1

Approximately 1.95 g

Answer 2

Answer:

The correct answer is option A.

Explanation:

Half life of the potassium-40 sample =$t_{\frac{1}{2}}= 1.277\times 10^9 years$

N = amount left after time t  = ?

Time = t =  $1.277\times 10^9 years$

$N_0$ = initial amount  = 500.3 g

$\lambda$ = rate constant

$\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{ 1.277\times 10^9 years}= 0.5426\times 10^{-9} year^{-1}$

$\log N=\log N_o\times -\frac{\lambda t}{2.303}$

$N = 1.95 g$

Hence, the correct answer is option A.