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

A 1.9

Step-by-step 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

Step-by-step 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