Question

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

Answer 1

60 days

Step-by-step explanation:

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.