A container is filled with a radioactive substance for which the half-life is $2$ days. A week later, when the container is opened, it contains $5 g$ of the substance. Approximately how may grams of the substances were initially placed in the container?

40

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60

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80

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100

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Solution

The correct option is D $60$
$N (t) = N_{o} e^{- λ t}$
$t_{1 / 2} = 2 d a y s$
$λ = \frac{l n 2}{t_{1 / 2}} = \frac{l n 2}{2}$
$N (t) = N_{o} e^{- λ t}$
At $t = 7$ days
$5 = N_{o} e^{- 7 \frac{l n 2}{2}}$
$N_{o} = 56.56 g m s \approx 60 g m s$

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A container is filled with a radioactive substance for which the half-life is 2 days. A week later, when the container is opened, it contains 5g of the substance. Approximately how may grams of the substances were initially placed in the container?

The correct option is D 60N(t)=Noe−λtt1/2=2 daysλ=ln2t1/2=ln22N(t)=Noe−λtAt t=7 days5=Noe−7ln22No=56.56 gms≈60 gms

A container is filled with a radioactive substance for which the half-life is $2$ days. A week later, when the container is opened, it contains $5 g$ of the substance. Approximately how may grams of the substances were initially placed in the container?

The correct option is D $60$
$N (t) = N_{o} e^{- λ t}$
$t_{1 / 2} = 2 d a y s$
$λ = \frac{l n 2}{t_{1 / 2}} = \frac{l n 2}{2}$
$N (t) = N_{o} e^{- λ t}$
At $t = 7$ days
$5 = N_{o} e^{- 7 \frac{l n 2}{2}}$
$N_{o} = 56.56 g m s \approx 60 g m s$