   # The curie (Ci) is a commonly used unit for measuring nuclear radioactivity: 1 curie of radiation is equal to 3.7 × 10 10 decay events per second (the number of decay events from 1 g radium in 1 s). a. What mass of Na 2 38 SO 4 has an activity of 10.0 mCi? Sulfur-38 has an atomic mass of 38.0 u and a half-life of 2.87 h. b. How long does it take for 99.99% of a sample of sulfur-38 to decay? ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 18, Problem 30E
Textbook Problem
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## The curie (Ci) is a commonly used unit for measuring nuclear radioactivity: 1 curie of radiation is equal to 3.7 × 1010 decay events per second (the number of decay events from 1 g radium in 1 s).a. What mass of Na2 38SO4 has an activity of 10.0 mCi? Sulfur-38 has an atomic mass of 38.0 u and a half-life of 2.87 h.b. How long does it take for 99.99% of a sample of sulfur-38 to decay?

(a)

Interpretation Introduction

Interpretation: Number of decay events per second in 1 curie of radiation is given. Mass of Na238SO4 that has an activity of 10.0mCi is to be determined.

Concept introduction: A process through which a unstable nuclide loses its energy due to excess of protons or neutrons is known as radioactive decay. The cause of instability of a nuclide is its inefficiency in holding the nucleus together. The curie is commonly used to measure nuclear radioactivity.

To determine: The mass of Na238SO4 that has an activity of 10.0mCi .

### Explanation of Solution

Explanation

The decay constant can be calculated by the formula given below.

λ=0.693t1/2

Where

• t1/2 is the half life of nuclide.
• λ is decay constant.

Substitute the value of half life in the above formula.

λ=0.6932.87×60×60s1=6.7073×10-5s-1_

Explanation

The decays corresponding to 1Ci of radiation = 3.7×1010decays per second

The decays corresponding to 10Ci of radiation = (10×3.7×1010)decays per second= 3.7×1011decays per second

Therefore, the number of molecules = 3.7×1011molecules

The formula to calculate rate =nλ

3.7×1011molecules=nλ

Where,

n is the number of molecules.

λ is the decay constant.

Substitute the value of the number of molecules in the above expression.

n=3.7×10116.7073×105=5.52×1015molecules_

The mass of Na238SO4 is 13

(b)

Interpretation Introduction

Interpretation: Time taken for 99.99% of a sample of sulfur- 38 to decay is to be calculated.

Concept introduction: A process through which a unstable nuclide loses its energy due to excess of protons or neutrons is known as radioactive decay. The cause of instability of a nuclide is its inefficiency in holding the nucleus together. The curie is commonly used to measure nuclear radioactivity.

To determine: The time taken by 99.99% sulfur- 38 to decay.

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