Question

In a radioactive substance Half-Life is 40 years about how much of a 30g sample was left after 160 years

A 1.9

B 3.8

C 7.5

D 15

Answer 1

Explanation:

Half-Life is 40 years so after 40 yrs, only 1/2 is left

160 years = 4 x 40 so it is 4 x half-life

so after 160 years, 30g sample left: 30 x 1/2 x 1/2 x 1/2 x 1/2

= 30 x 1/16

= 1.9

ans is A

Answer 2

A 1.9

Explanation:

Nt = No e^(-kt)

Where Nt is the ending amount

No is the starting amount

k is the decay constant

and t is the time

We need to determine the half life

Nt/No = e ^ -kt

1/2 of the original amount is left for 1/2 life. The time is 40 years. We will calculate k

1/2 = e ^ -k * 40

Take the natural log of each side

ln(1/2) = ln (e ^ -k * 40)

ln (1/2) = -40k

-ln(2) = -40k

ln 2 = 40k

1/40 ln (2) = k

Now we can calculate now much is left after 160 years of a 30 g sample

Nt = 30 e^(- 1/40 ln(2) * 160)

= 30 e^(-4ln(2))

= 15/8

=1.875