Chapter 42: Q. 50 (page 1237)

A $115 m C i$ radioactive tracer is made in a nuclear reactor. When it is delivered to a hospital hours later its activity is $95 m C i$ . The lowest usable level of activity is $10 m C i$ .
A. What is the tracer’s half-life?
B. For how long after delivery is the sample usable?

Short Answer

Expert verified

(a) Half-life of tracer is: $t_{\frac{1}{2}} = 58 h r$

(b) Max time with the sample being usable $t = 188.5 h r$

Step by step solution

Part(a): Step 1: Given information

We have been given that

$R_{o} = 115 mCi$

$t = 16 hr$

$R = 95 mCi$

Part(a) Step 2: Solving

Using the formula $R = R_{o} {(\frac{1}{2})}^{t / t_{1 / 2}}$

Substituting the given values $0.95 mCi = 1.15 mCi {(\frac{1}{2})}^{16 hr / t_{1 / 2}}$

Taking Natural log $\ln [\frac{0.95 mCi}{1.15 mCi}] = [\frac{16 hr}{t_{1 / 2}}] \ln (\frac{1}{2})$

Solving $t_{1 / 2} = \frac{16 hr}{0.27536} = 58.105 h r ≃ 58 h r$

Part(b) Step 1: Given information:

We need to find out the value of t for the sample.

Part (b) Step 2: Solving:

Using $R = R_{o} {(\frac{1}{2})}^{t / t_{1 / 2}}$ $(Where is R = 0.10 mCi)$

Substituting the given values $0.10 mCi = 0.95 mCi {(\frac{1}{2})}^{t / 58 hr}$

Taking natural log $\ln (\frac{0.10}{0.95}) = (\frac{t}{58 hr}) \ln (\frac{1}{2})$

Solving $3.25 = (\frac{t}{58 hr})$

$t = 188.5 hr$

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A $115 m C i$ radioactive tracer is made in a nuclear reactor. When it is delivered to a hospital hours later its activity is $95 m C i$ . The lowest usable level of activity is $10 m C i$ .
A. What is the tracer’s half-life?
B. For how long after delivery is the sample usable?

Short Answer

Step by step solution

Part(a): Step 1: Given information

Part(a) Step 2: Solving

Part(b) Step 1: Given information:

Part (b) Step 2: Solving:

One App. One Place for Learning.

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A 115mCiradioactive tracer is made in a nuclear reactor. When it is delivered to a hospital hours later its activity is 95mCi. The lowest usable level of activity is 10mCi.A. What is the tracer’s half-life?B. For how long after delivery is the sample usable?

Short Answer

Step by step solution

Part(a): Step 1: Given information

Part(a) Step 2: Solving

Part(b) Step 1: Given information:

Part (b) Step 2: Solving:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

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Study anywhere. Anytime. Across all devices.

A $115 m C i$ radioactive tracer is made in a nuclear reactor. When it is delivered to a hospital hours later its activity is $95 m C i$ . The lowest usable level of activity is $10 m C i$ .
A. What is the tracer’s half-life?
B. For how long after delivery is the sample usable?