Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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Question
![### Understanding Radioactive Decay: Half-Life Calculation
**Problem:**
A radioactive isotope has a half-life of 17.1 minutes. How long will it take for the radiation from a 325 pCi sample to decrease to 162 pCi?
**Concept:**
The half-life is the time required for a quantity to reduce to half its initial value. To find out how long it takes for the radiation to decrease from 325 pCi to 162 pCi, use the formula for half-life calculations:
\[ N(t) = N_0 \times \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}} \]
Where:
- \( N(t) \) is the remaining quantity of the substance.
- \( N_0 \) is the initial quantity of the substance.
- \( T_{1/2} \) is the half-life of the substance.
- \( t \) is the time elapsed.
**Steps:**
1. Substitute the known values into the formula.
2. Solve for \( t \).
This equation helps in determining the time it takes for the sample to decay from 325 pCi to 162 pCi, given its half-life.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3eb0d35-d0e7-4063-92cf-994346c5ae13%2F5eeeb889-2455-4a59-b89b-40255436eb44%2Fhtia8ep_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Radioactive Decay: Half-Life Calculation
**Problem:**
A radioactive isotope has a half-life of 17.1 minutes. How long will it take for the radiation from a 325 pCi sample to decrease to 162 pCi?
**Concept:**
The half-life is the time required for a quantity to reduce to half its initial value. To find out how long it takes for the radiation to decrease from 325 pCi to 162 pCi, use the formula for half-life calculations:
\[ N(t) = N_0 \times \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}} \]
Where:
- \( N(t) \) is the remaining quantity of the substance.
- \( N_0 \) is the initial quantity of the substance.
- \( T_{1/2} \) is the half-life of the substance.
- \( t \) is the time elapsed.
**Steps:**
1. Substitute the known values into the formula.
2. Solve for \( t \).
This equation helps in determining the time it takes for the sample to decay from 325 pCi to 162 pCi, given its half-life.
Expert Solution
Step 1
Radioactive decay follow first order kinetics
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