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The formula for the radius of an electron orbit is $r = \frac{n^2 h \epsilon_0}{\pi m e^2}$ or $r = 0.53 \times 10^{-10} \frac{n^2}{Z} ,$ Å
n^2 h ε₀ / π m e^2 or 0.53 × 10^{-10} n^2 / Z
What is the formula for potential energy of an electron in a shell?
V_{n} = \frac{ze^2}{2 h \epsilon_0 n^2}
The total energy of the electron is $T.E = -13.6 \frac{z^2}{n^2} \text{ eV}$
-13.6 z^2 / n^2
What is the kinetic energy formula for an electron in a shell?
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Potential energy (P.E) between two opposite charges is due to electrostatic potential energy.
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What is the derived formula for potential energy as per the additional notes?
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Which of the following formulas represents the potential energy in electron shells?
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Study Notes
Electron Orbit Radius
- The radius (r) of an electron's orbit is defined by
r = (n²hε₀) / (πme²)orr = 0.53 x 10⁻¹⁰ (n²/Z) Å, where:- n is the principal quantum number.
- h is Planck's constant.
- ε₀ is the permittivity of free space.
- m is the electron mass.
- e is the elementary charge.
- Z is the atomic number.
Electron Potential Energy
- The potential energy (Vn) of an electron in an orbit is given by
Vn = (ze²) / (2hε₀n²)orV₀,n = 2.18 x 10⁻¹⁸ (z/n) J, where:- z is the effective nuclear charge.
Electron Kinetic Energy
- The kinetic energy (KE) of an electron is
KE = (1/8)(me⁴)/(h²ε₀²n²)orKE = 13.6 (z²/n²) eV.
Electron Potential Energy (Electrostatic)
- The potential energy due to electrostatic interaction between two charges (q1 and q2) separated by distance r is
PE = (1/(4πε₀)) * (q1q2/r) = (1/(4πε₀))*e² = -(z²em²)/(4πε₀r). - This formula is applicable to oppositely charged particles.
Electron Derived Potential Energy
- A derived formula for potential energy is
PE = -2 * 13.6 (z²/n²) eV.
Electron Total Energy
- The total energy (TE) of an electron is
TE = -13.6 (z²/n²) eV.
Additional Considerations
- The electrostatic potential energy applies to oppositely charged particles.
- If considering masses, gravitational potential energy may need to be included.
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Description
This quiz covers the formulas related to the radius, potential energy, and kinetic energy of electrons in orbits. It explores important constants such as Planck's constant and the elementary charge. Test your understanding of these fundamental concepts in atomic physics.
