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14 June, 18:08

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

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Answers (2)
  1. 14 June, 18:14
    0
    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
  2. 14 June, 18:22
    0
    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
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