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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
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
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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.
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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