# Americium-241 is widely used in smoke detectors. The radiation released by this element ionizes particles that are then detected by a charged-particle collector. The half-life of 241 Am is 433 years, and it decays by emitting α particles. How many α particles are emitted each second by a 5.00-g sample of 241 Am?

### Chemistry: An Atoms First Approach

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

Chapter
Section

### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 18, Problem 26E
Textbook Problem
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## Americium-241 is widely used in smoke detectors. The radiation released by this element ionizes particles that are then detected by a charged-particle collector. The half-life of 241Am is 433 years, and it decays by emitting α particles. How many α particles are emitted each second by a 5.00-g sample of 241Am?

Interpretation Introduction

Interpretation:

Half-life of 241Am is given.  The number of alpha particles emitted each second by a 5.00g sample of 241Am is to be calculated.

Concept introduction:

Americium- 241 is used in smoke detectors. It decays by emitting α particles.  The radiation emitted by this element ionizes particles that are then detected by a charged particle collector.  Decay constant is the quantity that expresses the rate of decrease of number of atoms of a radioactive element per second.  Half-life of radioactive sample is defined as the time required for the number of nuclides to reach half of the original value.

### Explanation of Solution

Explanation

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

t1/2=0.693λ

Where

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

Half-life of 241Am is 433 years. Convert the years to seconds.

The conversion of 1 year to days is done as,

1year=365days

The conversion of days to hours is done as,

1day=24h

Therefore, the conversion of 365 days to hours is done as,

365day=(365×24)h=8760h

The conversion of hours to seconds is done as,

1h=3600s

Therefore, the conversion of 8760 hours to seconds is done as,

8760h=(8760×3600)s=31536000s

Hence, the conversion of 1year into seconds is done as,

1year=31536000s

Therefore, the conversion of 433years into seconds is done as,

433years=(433×31536000)s=1.3656×1010s

Substitute the value of Half-life in the t1/2 equation.

λ=0

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