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Calculate the energy in MeV equivalent to the rest mass of an electron . Given that the rest mass of an electron, m = 9.1×10−31kg, 1MeV = 1.6×10−13J and speed of light , c = 3×108ms−1.
Correct answer is '0.511'. Can you explain this answer?
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Verified Answer
Calculate the energy in MeV equivalent to the rest mass of an electron...
According to Einstein's mass-energy equivalence theory, E0=m0c2, where E0 is the rest mass energy, m0=9.11×10−31kg be the rest mass of the electron and c be the velocity of light.
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Calculate the energy in MeV equivalent to the rest mass of an electron...
Calculating the Energy Equivalent of Electron Mass
To calculate the energy equivalent of the rest mass of an electron, we will use the famous equation derived by Albert Einstein:
E = mc^2
where E is the energy, m is the mass, and c is the speed of light in a vacuum.
Step 1: Convert Mass to Kilograms
The given mass of the electron is 9.023 * 10^(-28) gm. We need to convert this mass to kilograms since the equation requires SI units. To do this, we divide the given mass by 1000:
9.023 * 10^(-28) gm = (9.023 * 10^(-28) / 1000) kg = 9.023 * 10^(-31) kg
Step 2: Plug Values into the Equation
Now that we have the mass in kilograms, we can substitute it into the equation along with the speed of light. The speed of light in a vacuum is approximately 3 * 10^8 meters per second:
E = (9.023 * 10^(-31) kg) * (3 * 10^8 m/s)^2
Step 3: Calculate the Energy
To simplify the calculation, we can first square the speed of light:
E = (9.023 * 10^(-31) kg) * (9 * 10^16 m^2/s^2)
Multiplying these values together gives:
E = 8.1207 * 10^(-14) kg * m^2/s^2
Step 4: Convert Energy to Electron Volts
To convert the energy from SI units to electron volts (eV), we use the conversion factor:
1 eV = 1.602 * 10^(-19) J
Dividing the energy by this conversion factor:
E = (8.1207 * 10^(-14) kg * m^2/s^2) / (1.602 * 10^(-19) J/eV)
Simplifying the expression gives:
E = 5.0727 * 10^(-5) kg * m^2/s^2 * eV/J
Step 5: Simplify the Units
To simplify the units, we can use the fact that 1 kg * m^2/s^2 is equivalent to 1 Joule (J). Therefore, the expression becomes:
E = 5.0727 * 10^(-5) eV
Final Answer:
Rounding to the appropriate number of significant figures, the energy equivalent of the rest mass of the electron is 0.5078 eV.
To calculate the energy equivalent of the rest mass of an electron, we will use the famous equation derived by Albert Einstein:
E = mc^2
where E is the energy, m is the mass, and c is the speed of light in a vacuum.
Step 1: Convert Mass to Kilograms
The given mass of the electron is 9.023 * 10^(-28) gm. We need to convert this mass to kilograms since the equation requires SI units. To do this, we divide the given mass by 1000:
9.023 * 10^(-28) gm = (9.023 * 10^(-28) / 1000) kg = 9.023 * 10^(-31) kg
Step 2: Plug Values into the Equation
Now that we have the mass in kilograms, we can substitute it into the equation along with the speed of light. The speed of light in a vacuum is approximately 3 * 10^8 meters per second:
E = (9.023 * 10^(-31) kg) * (3 * 10^8 m/s)^2
Step 3: Calculate the Energy
To simplify the calculation, we can first square the speed of light:
E = (9.023 * 10^(-31) kg) * (9 * 10^16 m^2/s^2)
Multiplying these values together gives:
E = 8.1207 * 10^(-14) kg * m^2/s^2
Step 4: Convert Energy to Electron Volts
To convert the energy from SI units to electron volts (eV), we use the conversion factor:
1 eV = 1.602 * 10^(-19) J
Dividing the energy by this conversion factor:
E = (8.1207 * 10^(-14) kg * m^2/s^2) / (1.602 * 10^(-19) J/eV)
Simplifying the expression gives:
E = 5.0727 * 10^(-5) kg * m^2/s^2 * eV/J
Step 5: Simplify the Units
To simplify the units, we can use the fact that 1 kg * m^2/s^2 is equivalent to 1 Joule (J). Therefore, the expression becomes:
E = 5.0727 * 10^(-5) eV
Final Answer:
Rounding to the appropriate number of significant figures, the energy equivalent of the rest mass of the electron is 0.5078 eV.
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Community Answer
Calculate the energy in MeV equivalent to the rest mass of an electron...
Rest mass of the electron m0 = 9.028 *10-28 gm.
∴ Energy equivalent =
= 81.252 x10-8 ergs
Now one electron volt = 1.6 * 10-12ergs
∴ Energy in electron volt
= 0.5078 -106 eV = 0.5078 MeV
(1 MeV = one million electron volts)
∴ Energy equivalent =
= 81.252 x10-8 ergs Now one electron volt = 1.6 * 10-12ergs
∴ Energy in electron volt
= 0.5078 -106 eV = 0.5078 MeV(1 MeV = one million electron volts)
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Calculate the energy in MeV equivalent to the rest mass of an electron . Given that the rest mass of an electron, m = 9.1×10−31kg,1MeV = 1.6×10−13Jand speed of light ,c = 3×108ms−1.Correct answer is '0.511'. Can you explain this answer?
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