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Phosphorus- 32 has a half-life of 14.0 days. A 40.0 g sample is being shipped. If it takes 28 days to arrive, how much P-32 remains upon delivery? Explain.

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User JuhaKangas
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Answer: 10.0 g of P-32 remains upon delivery.

Explanation: Radioactive decay is a process in which an unstable nucleus emits particles or energy and becomes more stable. Different radioactive substances have different rates of decay, which are measured by their half-lives. The half-life of a radioactive substance is the time it takes for half of its atoms to decay. For example, if we start with 100 atoms of a substance that has a half-life of 10 minutes, after 10 minutes we will have 50 atoms left, after 20 minutes we will have 25 atoms left, and so on.

To calculate the amount of a radioactive substance that remains after a certain time, we can use the formula:

A = A0 * (1/2)^(t/T)

where A is the final amount, A0 is the initial amount, t is the time elapsed, and T is the half-life. This formula is based on the idea that every half-life, the amount of the substance decreases by half. For example, if we start with 100 g of a substance that has a half-life of 10 minutes, after 10 minutes we will have 100 * (1/2)^(10/10) = 100 * (1/2)^1 = 50 g left, after 20 minutes we will have 100 * (1/2)^(20/10) = 100 * (1/2)^2 = 25 g left, and so on.

In this problem, we are given that A0 = 40.0 g, t = 28 days, and T = 14.0 days. Plugging these values into the formula, we get:

A = 40.0 * (1/2)^(28/14) A = 40.0 * (1/2)^2 A = 40.0 * 0.25 A = 10.0 g

Therefore, 10.0 g of P-32 remains upon delivery.

Hope this helps, and have a great day! =)

User Benjamin Collins
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