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

The correct answer is option A.

Step-by-step explanation:

Half life of the potassium-40 sample =
`t_{(1)/(2)}= 1.277* 10^9 years`

N = amount left after time t = ?

Time = t =
`1.277* 10^9 years`

`N_0` = initial amount = 500.3 g

`\lambda` = rate constant

`\lambda =\frac{0.693}{t_{(1)/(2)}}=(0.693)/( 1.277* 10^9 years)= 0.5426* 10^(-9) year^(-1)`

`\log N=\log N_o* -(\lambda t)/(2.303)`

`N = 1.95 g`

Hence, the correct answer is option A.