The energy equivalent of mass associated with the rest mass of an electron, is nearly:
0.51 MeV
The question asks about the energy equivalent of the rest mass of an electron. This concept is fundamental in physics and is directly explained by Einstein's famous mass-energy equivalence principle.
Energy Equivalent Principle
According to Albert Einstein's special theory of relativity, mass and energy are interchangeable. This relationship is expressed by the famous equation:
\[ E = mc^2 \]
Where:
- \(E\) represents the energy.
- \(m\) represents the mass.
- \(c\) represents the speed of light in a vacuum.
This equation tells us that a certain amount of mass, even when at rest, possesses an equivalent amount of energy. The energy associated with the rest mass of a particle is often referred to as its rest mass energy.
Electron Rest Mass Calculation
To calculate the energy equivalent of the rest mass of an electron, we need the following standard values:
- Rest mass of an electron (\(m_e\)): \(9.109 \times 10^{-31}\) kg
- Speed of light in vacuum (\(c\)): \(2.998 \times 10^8\) m/s
- Conversion factor from Joules to electron volts (eV): \(1 \text{ eV} = 1.602 \times 10^{-19}\) J
- Conversion factor from electron volts to Mega electron volts (MeV): \(1 \text{ MeV} = 10^6 \text{ eV}\)
Step-by-step Calculation:
- Calculate \(c^2\): \[ c^2 = (2.998 \times 10^8 \text{ m/s})^2 \] \[ c^2 \approx 8.988 \times 10^{16} \text{ m}^2/\text{s}^2 \]
- Calculate the energy \(E\) in Joules (J) using \(E = m_e c^2\): \[ E = (9.109 \times 10^{-31} \text{ kg}) \times (8.988 \times 10^{16} \text{ m}^2/\text{s}^2) \] \[ E \approx 8.187 \times 10^{-14} \text{ J} \]
- Convert the energy from Joules to electron volts (eV): \[ E_{\text{eV}} = \frac{8.187 \times 10^{-14} \text{ J}}{1.602 \times 10^{-19} \text{ J/eV}} \] \[ E_{\text{eV}} \approx 5.110 \times 10^5 \text{ eV} \]
- Convert the energy from electron volts (eV) to Mega electron volts (MeV): \[ E_{\text{MeV}} = \frac{5.110 \times 10^5 \text{ eV}}{10^6 \text{ eV/MeV}} \] \[ E_{\text{MeV}} \approx 0.511 \text{ MeV} \]
Therefore, the energy equivalent of the rest mass of an electron is approximately 0.511 MeV.
Comparing this calculated value with the given options:
- 1.02 MeV
- 0.51 MeV
- 2.04 MeV
- 931.5 MeV
The calculated value of approximately 0.511 MeV is very close to 0.51 MeV, which is one of the options.
Important Questions from Nucleus
- The binding energy B of a nucleus is approximated by the formula B = a 1 A − a 2 A 2/3 − a 3 Z 2 A −1/3 − a 4 (A − 2Z) 2 A −1 where Z is the atomic number and A is the mass number of the nucleus. If \(\rm\frac{a_4}{a_3}\) ≃ 30, the atomic number Z for naturally stable isobars (constant value of A) is
What are the main constituents of biogas?
- Considering that the radius of an atomic nucleus, $R$, can be approximated by the formula $R = R_0 A^{1/3}$, where $R_0 \approx 1.2 \times 10^{-15}$ m is the Fermi radius constant and $A$ is the mass number, and the average mass of a single nucleon is approximately $1.67 \times 10^{-27}$ kg. Calculate the approximate order of magnitude of nuclear matter density in $\text{kg/m}^3$.
- The mass number of argon is 40. Which one of the following statements is correct?
The difference in mass of a nucleus and its constituent nucleons is called the ____________.
