SATHEE: Atoms And Nuclei Question 387

Atoms And Nuclei Question 387

Question: 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 many grams of the substance were initially placed in the container?

Options:

A) 40

B) 60

C) 80

D) 100

Show Answer

Answer:

Correct Answer: C

Solution:

For this substance 7 days correspond to $3.5$ half- lives. Over 3 half- lifes the sample reduces to $\frac{1}{2^{3}} = \frac{1}{8}$ of its initial mass. After 4 half- lifes, the sample has only $\frac{1}{2^{4}} = \frac{1}{16}$ of its initial mass. Hence, after $3.5$ half- lives the sample must contain somewhere between $1 / 8$ and $1 / 16$ of its initial mass. Hence 5 g is somewhere between 1/8 and $1 / 16$ of the initial mass. So, the initial mass is somewhere between $8 \times 5 = 40 g$ and $16 \times 5 = 80 g .$

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Atoms And Nuclei Question 387

Question: 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 many grams of the substance were initially placed in the container?

Options:

Answer:

Solution:

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