Chapter 5: Q. 5.67 (page 165)

A $120 - m g$ sample of technetium-role="math" localid="1652175464491" $99 m$ is used for a diagnostic test. If technetium- $99 m$ has a half-life of $6.0 h$ . how many milligrams of the technetium- $99 m$ sample remains active $24 h$ after the test? $(5, 4)$

Short Answer

Expert verified

The value of the expression is $\frac{1}{16}$ .

Step by step solution

Step 1- Given information

We are given that

$N_{0} = 120 mg, t = 24 hr, t_{\frac{1}{2}} = 6.0 hr N = ?$

The amount of radioactive sample (N) is known to remain after the $n$ half-life $= \frac{N_{0}}{2^{n}}$

$N_{e} =$ initial amount of radioactive material

$N = Number of half periods = \frac{t}{t_{\frac{1}{2}}}$

Step 2- Explanation

Replace the value of the expression

$\frac{N}{N_{0}} = {(\frac{1}{2})}^{\frac{1}{t_{1}}}$

$\frac{N}{120 mg} = {(\frac{1}{2})}^{\frac{24 mr}{6.04 r}}$

$\frac{N}{120 mg} = {(\frac{1}{2})}^{4}$

or $\frac{N}{120 mg} = \frac{1}{16}$

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A $120 - m g$ sample of technetium-role="math" localid="1652175464491" $99 m$ is used for a diagnostic test. If technetium- $99 m$ has a half-life of $6.0 h$ . how many milligrams of the technetium- $99 m$ sample remains active $24 h$ after the test? $(5, 4)$

Short Answer

Step by step solution

Step 1- Given information

Step 2- Explanation

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A 120-mgsample of technetium-role="math" localid="1652175464491" 99mis used for a diagnostic test. If technetium- 99mhas a half-life of 6.0h. how many milligrams of the technetium-99msample remains active 24hafter the test? (5,4)

Short Answer

Step by step solution

Step 1- Given information

Step 2- Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

Making Measurements

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Study anywhere. Anytime. Across all devices.

A $120 - m g$ sample of technetium-role="math" localid="1652175464491" $99 m$ is used for a diagnostic test. If technetium- $99 m$ has a half-life of $6.0 h$ . how many milligrams of the technetium- $99 m$ sample remains active $24 h$ after the test? $(5, 4)$