Radius of Orbit given Total Energy of Electron Solution

STEP 0: Pre-Calculation Summary
Formula Used
Radius of Orbit = (-(Atomic Number*([Charge-e]^2))/(2*Total Energy))
rorbit = (-(Z*([Charge-e]^2))/(2*Etotal))
This formula uses 1 Constants, 3 Variables
Constants Used
[Charge-e] - Charge of electron Value Taken As 1.60217662E-19
Variables Used
Radius of Orbit - (Measured in Meter) - Radius of Orbit is the distance from the center of orbit of an electron to a point on its surface.
Atomic Number - Atomic Number is the number of protons present inside the nucleus of an atom of an element.
Total Energy - (Measured in Joule) - Total Energy is the sum of the kinetic energy and the potential energy of the system under consideration.
STEP 1: Convert Input(s) to Base Unit
Atomic Number: 17 --> No Conversion Required
Total Energy: 900 Joule --> 900 Joule No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rorbit = (-(Z*([Charge-e]^2))/(2*Etotal)) --> (-(17*([Charge-e]^2))/(2*900))
Evaluating ... ...
rorbit = -2.42436048158159E-40
STEP 3: Convert Result to Output's Unit
-2.42436048158159E-40 Meter -->-2.42436048158159E-31 Nanometer (Check conversion here)
FINAL ANSWER
-2.42436048158159E-31 โ‰ˆ -2.4E-31 Nanometer <-- Radius of Orbit
(Calculation completed in 00.004 seconds)

Credits

Created by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
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25 Structure of Atom Calculators

Bragg equation for Wavelength of Atoms in Crystal Lattice
Go Wavelength of X-ray = 2*Interplanar Spacing of Crystal*(sin(Bragg's Angle of Crystal))/Order of Diffraction
Bragg Equation for Distance between Planes of Atoms in Crystal Lattice
Go Interplanar Spacing in nm = (Order of Diffraction*Wavelength of X-ray)/(2*sin(Bragg's Angle of Crystal))
Bragg Equation for Order of Diffraction of Atoms in Crystal Lattice
Go Order of Diffraction = (2*Interplanar Spacing in nm*sin(Bragg's Angle of Crystal))/Wavelength of X-ray
Mass of Moving Electron
Go Mass of Moving Electron = Rest Mass of Electron/sqrt(1-((Velocity of Electron/[c])^2))
Electrostatic Force between Nucleus and Electron
Go Force between n and e = ([Coulomb]*Atomic Number*([Charge-e]^2))/(Radius of Orbit^2)
Energy of Stationary States
Go Energy of Stationary States = [Rydberg]*((Atomic Number^2)/(Quantum Number^2))
Radii of Stationary States
Go Radii of Stationary States = [Bohr-r]*((Quantum Number^2)/Atomic Number)
Radius of Orbit given Time Period of Electron
Go Radius of Orbit = (Time Period of Electron*Velocity of Electron)/(2*pi)
Time Period of Revolution of Electron
Go Time Period of Electron = (2*pi*Radius of Orbit)/Velocity of Electron
Orbital Frequency given Velocity of Electron
Go Frequency using Energy = Velocity of Electron/(2*pi*Radius of Orbit)
Total Energy in Electron Volts
Go Kinetic Energy of Photon = (6.8/(6.241506363094*10^(18)))*(Atomic Number)^2/(Quantum Number)^2
Energy in Electron Volts
Go Kinetic Energy of Photon = (6.8/(6.241506363094*10^(18)))*(Atomic Number)^2/(Quantum Number)^2
Kinetic Energy in Electron Volts
Go Energy of an Atom = -(13.6/(6.241506363094*10^(18)))*(Atomic Number)^2/(Quantum Number)^2
Radius of Orbit given Potential Energy of Electron
Go Radius of Orbit = (-(Atomic Number*([Charge-e]^2))/Potential Energy of Electron)
Energy of Electron
Go Kinetic Energy of Photon = 1.085*10^-18*(Atomic Number)^2/(Quantum Number)^2
Wave Number of Moving Particle
Go Wave Number = Energy of Atom/([hP]*[c])
Kinetic Energy of Electron
Go Energy of Atom = -2.178*10^(-18)*(Atomic Number)^2/(Quantum Number)^2
Radius of Orbit given Total Energy of Electron
Go Radius of Orbit = (-(Atomic Number*([Charge-e]^2))/(2*Total Energy))
Radius of Orbit given Kinetic Energy of Electron
Go Radius of Orbit = (Atomic Number*([Charge-e]^2))/(2*Kinetic Energy)
Angular Velocity of Electron
Go Angular Velocity Electron = Velocity of Electron/Radius of Orbit
Mass Number
Go Mass Number = Number of Protons+Number of Neutrons
Electric Charge
Go Electric Charge = Number of Electron*[Charge-e]
Number of Neutrons
Go Number of Neutrons = Mass Number-Atomic Number
Specific Charge
Go Specific Charge = Charge/[Mass-e]
Wave Number of Electromagnetic Wave
Go Wave Number = 1/Wavelength of Light Wave

Radius of Orbit given Total Energy of Electron Formula

Radius of Orbit = (-(Atomic Number*([Charge-e]^2))/(2*Total Energy))
rorbit = (-(Z*([Charge-e]^2))/(2*Etotal))

What is Bohr's model?

Bohr's Theory is a theory of atomic structure in which the hydrogen atom (Bohr atom ) is assumed to consist of a proton as nucleus, with a single electron moving in distinct circular orbits around it, each orbit corresponding to a specific quantized energy state: the theory was extended to other atoms.

How to Calculate Radius of Orbit given Total Energy of Electron?

Radius of Orbit given Total Energy of Electron calculator uses Radius of Orbit = (-(Atomic Number*([Charge-e]^2))/(2*Total Energy)) to calculate the Radius of Orbit, The Radius of orbit given total energy of electron is defined as the radius of the fixed orbit as the electron revolves around the nucleus of the atom. Radius of Orbit is denoted by rorbit symbol.

How to calculate Radius of Orbit given Total Energy of Electron using this online calculator? To use this online calculator for Radius of Orbit given Total Energy of Electron, enter Atomic Number (Z) & Total Energy (Etotal) and hit the calculate button. Here is how the Radius of Orbit given Total Energy of Electron calculation can be explained with given input values -> -2.4E-22 = (-(17*([Charge-e]^2))/(2*900)).

FAQ

What is Radius of Orbit given Total Energy of Electron?
The Radius of orbit given total energy of electron is defined as the radius of the fixed orbit as the electron revolves around the nucleus of the atom and is represented as rorbit = (-(Z*([Charge-e]^2))/(2*Etotal)) or Radius of Orbit = (-(Atomic Number*([Charge-e]^2))/(2*Total Energy)). Atomic Number is the number of protons present inside the nucleus of an atom of an element & Total Energy is the sum of the kinetic energy and the potential energy of the system under consideration.
How to calculate Radius of Orbit given Total Energy of Electron?
The Radius of orbit given total energy of electron is defined as the radius of the fixed orbit as the electron revolves around the nucleus of the atom is calculated using Radius of Orbit = (-(Atomic Number*([Charge-e]^2))/(2*Total Energy)). To calculate Radius of Orbit given Total Energy of Electron, you need Atomic Number (Z) & Total Energy (Etotal). With our tool, you need to enter the respective value for Atomic Number & Total Energy 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 Radius of Orbit?
In this formula, Radius of Orbit uses Atomic Number & Total Energy. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • Radius of Orbit = (Atomic Number*([Charge-e]^2))/(2*Kinetic Energy)
  • Radius of Orbit = (-(Atomic Number*([Charge-e]^2))/Potential Energy of Electron)
  • Radius of Orbit = (Time Period of Electron*Velocity of Electron)/(2*pi)
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