Calculate to four significant figures a. the mass defect in kg, and b. the energy released in kJ/mol, when a neutron decays to produce a proton and an electron. The neutron, proton, and electron masses are 1.67493 x 10–27 kg, 1.67262 × 10–27 kg and 9.10939 x 10–31 kg, respectively.
Calculate to four significant figures a. the mass defect in kg, and b. the energy released in kJ/mol, when a neutron decays to produce a proton and an electron. The neutron, proton, and electron masses are 1.67493 x 10–27 kg, 1.67262 × 10–27 kg and 9.10939 x 10–31 kg, respectively.
Chemistry
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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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![### Neutron Decay Calculations
#### Calculate to four significant figures:
a. **The mass defect in kg, and**
b. **The energy released in kJ/mol, when a neutron decays to produce a proton and an electron.**
The neutron, proton, and electron masses are:
- Neutron mass: \(1.67493 \times 10^{-27} \, \text{kg}\)
- Proton mass: \(1.67262 \times 10^{-27} \, \text{kg}\)
- Electron mass: \(9.10939 \times 10^{-31} \, \text{kg}\)
---
**To calculate the mass defect and the energy released during the decay process:**
1. **Determine the mass defect (\(\Delta m\)):**
\[
\Delta m = \text{Mass of neutron} - (\text{Mass of proton} + \text{Mass of electron})
\]
2. **Convert the mass defect to energy using Einstein's equation (\(E = \Delta m c^2\)):**
\[
E = \Delta m c^2
\]
where \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)).
3. **Then, convert the energy per decay to kJ/mol:**
\[
\text{Energy per mol} = \left( \frac{E}{1.60218 \times 10^{-19} \, \text{J/eV}} \right) \times (6.022 \times 10^{23} \, \text{particles/mol})
\]
By following the steps above, you can determine the mass defect and the energy released when a neutron decays into a proton and an electron.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74279ea1-eff5-4403-94c6-eaa833f0d034%2F7bdd3a17-1b77-4982-8030-99092f65a9d9%2Fmmc1m93.png&w=3840&q=75)
Transcribed Image Text:### Neutron Decay Calculations
#### Calculate to four significant figures:
a. **The mass defect in kg, and**
b. **The energy released in kJ/mol, when a neutron decays to produce a proton and an electron.**
The neutron, proton, and electron masses are:
- Neutron mass: \(1.67493 \times 10^{-27} \, \text{kg}\)
- Proton mass: \(1.67262 \times 10^{-27} \, \text{kg}\)
- Electron mass: \(9.10939 \times 10^{-31} \, \text{kg}\)
---
**To calculate the mass defect and the energy released during the decay process:**
1. **Determine the mass defect (\(\Delta m\)):**
\[
\Delta m = \text{Mass of neutron} - (\text{Mass of proton} + \text{Mass of electron})
\]
2. **Convert the mass defect to energy using Einstein's equation (\(E = \Delta m c^2\)):**
\[
E = \Delta m c^2
\]
where \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)).
3. **Then, convert the energy per decay to kJ/mol:**
\[
\text{Energy per mol} = \left( \frac{E}{1.60218 \times 10^{-19} \, \text{J/eV}} \right) \times (6.022 \times 10^{23} \, \text{particles/mol})
\]
By following the steps above, you can determine the mass defect and the energy released when a neutron decays into a proton and an electron.
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