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Energy of an electron in elliptical orbit Solution

STEP 0: Pre-Calculation Summary
Formula Used
energy = (-((Atomic number^2)*[Mass-e]*([Charge-e]^4))/(8*([Permitivity-vacuum]^2)*([hP]^2)*(Quantum Number^2)))
e = (-((Z^2)*[Mass-e]*([Charge-e]^4))/(8*([Permitivity-vacuum]^2)*([hP]^2)*(n^2)))
This formula uses 5 Constants, 1 Functions, 2 Variables
Constants Used
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
[hP] - Planck constant Value Taken As 6.626070040E-34 kilogram Meter² / Second
[Charge-e] - Charge of electron Value Taken As 1.60217662E-19
[Mass-e] - Mass of electron Value Taken As 9.10938356E-31
[Permitivity-vacuum] - Permittivity of vacuum Value Taken As 8.85E-12
Functions Used
C - Binomial coefficient function, C(n,k)
Variables Used
Atomic number- Atomic number is the number of protons present inside the nucleus of an atom of an element.
Quantum Number- Quantum Number describe values of conserved quantities in the dynamics of a quantum system.
STEP 1: Convert Input(s) to Base Unit
Atomic number: 17 --> No Conversion Required
Quantum Number: 1 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
e = (-((Z^2)*[Mass-e]*([Charge-e]^4))/(8*([Permitivity-vacuum]^2)*([hP]^2)*(n^2))) --> (-((17^2)*[Mass-e]*([Charge-e]^4))/(8*([Permitivity-vacuum]^2)*([hP]^2)*(1^2)))
Evaluating ... ...
e = -6.30579457511871E-16
STEP 3: Convert Result to Output's Unit
-6.30579457511871E-16 Joule --> No Conversion Required
FINAL ANSWER
-6.30579457511871E-16 Joule <-- Energy
(Calculation completed in 00.002 seconds)

9 Sommerfeld model Calculators

Energy of an electron in elliptical orbit
energy = (-((Atomic number^2)*[Mass-e]*([Charge-e]^4))/(8*([Permitivity-vacuum]^2)*([hP]^2)*(Quantum Number^2))) Go
Angular momentum of electron
angular_momentum = (Minor axis of elliptical orbit*[hP])/(2*pi) Go
Total momentum of electrons in the elliptical orbit
total_momentum = sqrt((Angular Momentum^2)+(Radial momentum^2)) Go
Radial momentum of electron given angular momentum
radial_momentum = sqrt((Total momentum^2)-(Angular Momentum^2)) Go
Angular momentum of electron given radial momentum
angular_momentum = sqrt((Total momentum^2)-(Radial momentum^2)) Go
Radial momentum of an electron
radial_momentum = (Radial quantization number*[hP])/(2*pi) Go
Angular quantization number of electron in elliptical orbit
angular_quantization_number = Quantum Number-Radial quantization number Go
Radial quantization number of electron in elliptical orbit
radial_quantization_number = Quantum Number-Angular quantization number Go
Quantum number of electron in elliptical orbit
quantum_number = Radial quantization number+Angular quantization number Go

Energy of an electron in elliptical orbit Formula

energy = (-((Atomic number^2)*[Mass-e]*([Charge-e]^4))/(8*([Permitivity-vacuum]^2)*([hP]^2)*(Quantum Number^2)))
e = (-((Z^2)*[Mass-e]*([Charge-e]^4))/(8*([Permitivity-vacuum]^2)*([hP]^2)*(n^2)))

What is Sommerfeld atomic model?

Sommerfeld model was proposed to explain the fine spectrum. Sommerfeld predicted that electrons revolve in elliptical orbits as well as circular orbits. During the motion of electrons in a circular orbit, the only angle of revolution changes while the distance from the nucleus remains the same but in an elliptical orbit, both are changed. The distance from the nucleus is termed as radius vector and the angle of revolution predicted is the azimuthal angle.

How to Calculate Energy of an electron in elliptical orbit?

Energy of an electron in elliptical orbit calculator uses energy = (-((Atomic number^2)*[Mass-e]*([Charge-e]^4))/(8*([Permitivity-vacuum]^2)*([hP]^2)*(Quantum Number^2))) to calculate the Energy, The Energy of an electron in elliptical orbit is defined as is the energy consumed by a particle/electron to move in an elliptical orbit. Energy and is denoted by e symbol.

How to calculate Energy of an electron in elliptical orbit using this online calculator? To use this online calculator for Energy of an electron in elliptical orbit, enter Atomic number (Z) and Quantum Number (n) and hit the calculate button. Here is how the Energy of an electron in elliptical orbit calculation can be explained with given input values -> -6.306E-16 = (-((17^2)*[Mass-e]*([Charge-e]^4))/(8*([Permitivity-vacuum]^2)*([hP]^2)*(1^2))).

FAQ

What is Energy of an electron in elliptical orbit?
The Energy of an electron in elliptical orbit is defined as is the energy consumed by a particle/electron to move in an elliptical orbit and is represented as e = (-((Z^2)*[Mass-e]*([Charge-e]^4))/(8*([Permitivity-vacuum]^2)*([hP]^2)*(n^2))) or energy = (-((Atomic number^2)*[Mass-e]*([Charge-e]^4))/(8*([Permitivity-vacuum]^2)*([hP]^2)*(Quantum Number^2))). Atomic number is the number of protons present inside the nucleus of an atom of an element and Quantum Number describe values of conserved quantities in the dynamics of a quantum system.
How to calculate Energy of an electron in elliptical orbit?
The Energy of an electron in elliptical orbit is defined as is the energy consumed by a particle/electron to move in an elliptical orbit is calculated using energy = (-((Atomic number^2)*[Mass-e]*([Charge-e]^4))/(8*([Permitivity-vacuum]^2)*([hP]^2)*(Quantum Number^2))). To calculate Energy of an electron in elliptical orbit, you need Atomic number (Z) and Quantum Number (n). With our tool, you need to enter the respective value for Atomic number and Quantum Number and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Energy?
In this formula, Energy uses Atomic number and Quantum Number. We can use 9 other way(s) to calculate the same, which is/are as follows -
  • total_momentum = sqrt((Angular Momentum^2)+(Radial momentum^2))
  • energy = (-((Atomic number^2)*[Mass-e]*([Charge-e]^4))/(8*([Permitivity-vacuum]^2)*([hP]^2)*(Quantum Number^2)))
  • radial_momentum = (Radial quantization number*[hP])/(2*pi)
  • quantum_number = Radial quantization number+Angular quantization number
  • angular_momentum = (Minor axis of elliptical orbit*[hP])/(2*pi)
  • radial_quantization_number = Quantum Number-Angular quantization number
  • angular_quantization_number = Quantum Number-Radial quantization number
  • radial_momentum = sqrt((Total momentum^2)-(Angular Momentum^2))
  • angular_momentum = sqrt((Total momentum^2)-(Radial momentum^2))
Where is the Energy of an electron in elliptical orbit calculator used?
Among many, Energy of an electron in elliptical orbit calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}
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