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fgiga [73]
2 years ago
9

How long will it take for 475 mg of a sample of radium-225, which has a half-life of about 15 days, to decay to 30 mg

SAT
1 answer:
zlopas [31]2 years ago
7 0
<h3>Answer:</h3>

60 days

<h3>Explanation:</h3>

Half-life is the amount of time it takes half of a substance to decay away.

Guess and Check

One method for solving half-life problems like this is to guess and check. To do this, we can continue to divide 475mg by 2 until we get to 30mg.

  • 475 ÷ 2 = 237.5
  • 237.5 ÷ 2 = 118.75
  • 118.75 ÷ 2 = 59.375
  • 59.375 ÷ 2 = 29.6875

As seen here, it takes approximately 4 half-lives for this sample of Ra-225 to decay to 30mg. Now, we can multiply 4 by the length of the half-life, 15 days.

  • 4 * 15 = 60 days.

Fractions

Another way to solve this is to use fractions.

  • 30 is about 1/16 of 475
  • 16 is equivalent to 2^{4}.

This means that it takes 4 half-lives for 475mg to decay to 30mg. Using the same method above, we can tell that 4 half-lives are 60 days.

Important Note

In this question, I rounded occasionally. So, not all of the values are exact, but they are all very close.

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