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Radius of Bohr's Orbit Calculator

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✖Quantum Number describe values of conserved quantities in the dynamics of a quantum system.ⓘ Quantum Number [nquantum]
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✖Atomic Number is the number of protons present inside the nucleus of an atom of an element.ⓘ Atomic Number [Z]
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✖Radius of Orbit given AN is the distance from the center of orbit of an electron to a point on its surface.ⓘ Radius of Bohr's Orbit [rorbit_AN]
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Radius of Bohr's Orbit

Formula
`"r"_{"orbit_AN"} = (("n"_{"quantum"}^2)*("[hP]"^2))/(4*(pi^2)*"[Mass-e]"*"[Coulomb]"*"Z"*("[Charge-e]"^2))`

Example
`"0.19922nm"=((("8")^2)*("[hP]"^2))/(4*(pi^2)*"[Mass-e]"*"[Coulomb]"*"17"*("[Charge-e]"^2))`

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Radius of Bohr's Orbit Solution

STEP 0: Pre-Calculation Summary
Formula Used
Radius of Orbit given AN = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*Atomic Number*([Charge-e]^2))
rorbit_AN = ((nquantum^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*Z*([Charge-e]^2))
This formula uses 5 Constants, 3 Variables
Constants Used
[Charge-e] - Charge of electron Value Taken As 1.60217662E-19
[Coulomb] - Coulomb constant Value Taken As 8.9875E+9
[Mass-e] - Mass of electron Value Taken As 9.10938356E-31
[hP] - Planck constant Value Taken As 6.626070040E-34
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Radius of Orbit given AN - (Measured in Meter) - Radius of Orbit given AN is the distance from the center of orbit of an electron to a point on its surface.
Quantum Number - Quantum Number describe values of conserved quantities in the dynamics of a quantum system.
Atomic Number - Atomic Number is the number of protons present inside the nucleus of an atom of an element.
STEP 1: Convert Input(s) to Base Unit
Quantum Number: 8 --> No Conversion Required
Atomic Number: 17 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rorbit_AN = ((nquantum^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*Z*([Charge-e]^2)) --> ((8^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*17*([Charge-e]^2))
Evaluating ... ...
rorbit_AN = 1.99219655831311E-10
STEP 3: Convert Result to Output's Unit
1.99219655831311E-10 Meter -->0.199219655831311 Nanometer (Check conversion here)
FINAL ANSWER
0.199219655831311 ≈ 0.19922 Nanometer <-- Radius of Orbit given AN
(Calculation completed in 00.004 seconds)
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Credits

Created by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
Akshada Kulkarni has created this Calculator and 500+ more calculators!
Verified by Suman Ray Pramanik
Indian Institute of Technology (IIT), Kanpur
Suman Ray Pramanik has verified this Calculator and 100+ more calculators!

8 Radius of Bohr's Orbit Calculators

Radius of Bohr's Orbit
Go Radius of Orbit given AN = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*Atomic Number*([Charge-e]^2))
Radius of Orbit
Go Radius of an Orbit = (Quantum Number*[hP])/(2*pi*Mass*Velocity)
Radius of Bohr's Orbit for Hydrogen Atom
Go Radius of Orbit given AV = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2))
Angular Momentum using Radius of Orbit
Go Angular Momentum using Radius Orbit = Atomic Mass*Velocity*Radius of Orbit
Radius of Bohr's Orbit given Atomic Number
Go Radius of Orbit given AN = ((0.529/10000000000)*(Quantum Number^2))/Atomic Number
Bohr's Radius
Go Bohr Radius of an Atom = (Quantum Number/Atomic Number)*0.529*10^(-10)
Radius of Orbit given Angular Velocity
Go Radius of Orbit given AV = Velocity of Electron/Angular Velocity
Frequency using Energy
Go Frequency using Energy = 2*Energy of Atom/[hP]

12 Important Formulas on Bohr's Atomic Model Calculators

Change in Wave Number of Moving Particle
Go Wave Number of moving Particle = 1.097*10^7*((Final Quantum Number)^2-(Initial Quantum Number)^2)/((Final Quantum Number^2)*(Initial Quantum Number^2))
Radius of Bohr's Orbit
Go Radius of Orbit given AN = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*Atomic Number*([Charge-e]^2))
Internal Energy of Ideal Gas using Law of Equipartition Energy
Go Internal Molar Energy given EP = (Degree of Freedom/2)*Number of Moles*[R]*Temperature of Gas
Velocity of Electron given Time Period of Electron
Go Velocity of Electron given Time = (2*pi*Radius of Orbit)/Time Period of Electron
Angular Momentum using Radius of Orbit
Go Angular Momentum using Radius Orbit = Atomic Mass*Velocity*Radius of Orbit
Radius of Bohr's Orbit given Atomic Number
Go Radius of Orbit given AN = ((0.529/10000000000)*(Quantum Number^2))/Atomic Number
Energy of Electron in Final Orbit
Go Energy of Electron in Orbit = (-([Rydberg]/(Final Quantum Number^2)))
Energy of Electron in Initial Orbit
Go Energy of Electron in Orbit = (-([Rydberg]/(Initial Orbit^2)))
Atomic Mass
Go Atomic Mass = Total Mass of Proton+Total Mass of Neutron
Number of Electrons in nth Shell
Go Number of Electrons in nth Shell = (2*(Quantum Number^2))
Number of Orbitals in nth Shell
Go Number of Orbitals in nth Shell = (Quantum Number^2)
Orbital Frequency of Electron
Go Orbital Frequency = 1/Time Period of Electron

Radius of Bohr's Orbit Formula

Radius of Orbit given AN = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*Atomic Number*([Charge-e]^2))
rorbit_AN = ((nquantum^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*Z*([Charge-e]^2))

What is Bohr's theory?

A theory of atomic structure in which the hydrogen atom (Bohr atom ) is assumed to consist of a proton as the 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 Bohr's Orbit?

Radius of Bohr's Orbit calculator uses Radius of Orbit given AN = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*Atomic Number*([Charge-e]^2)) to calculate the Radius of Orbit given AN, The Radius of Bohr's orbit formula is defined as a physical constant, expressing the most probable distance between the electron and the nucleus in a Hydrogen atom. Radius of Orbit given AN is denoted by rorbit_AN symbol.

How to calculate Radius of Bohr's Orbit using this online calculator? To use this online calculator for Radius of Bohr's Orbit, enter Quantum Number (nquantum) & Atomic Number (Z) and hit the calculate button. Here is how the Radius of Bohr's Orbit calculation can be explained with given input values -> 2E+8 = ((8^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*17*([Charge-e]^2)).

FAQ

What is Radius of Bohr's Orbit?
The Radius of Bohr's orbit formula is defined as a physical constant, expressing the most probable distance between the electron and the nucleus in a Hydrogen atom and is represented as rorbit_AN = ((nquantum^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*Z*([Charge-e]^2)) or Radius of Orbit given AN = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*Atomic Number*([Charge-e]^2)). Quantum Number describe values of conserved quantities in the dynamics of a quantum system & Atomic Number is the number of protons present inside the nucleus of an atom of an element.
How to calculate Radius of Bohr's Orbit?
The Radius of Bohr's orbit formula is defined as a physical constant, expressing the most probable distance between the electron and the nucleus in a Hydrogen atom is calculated using Radius of Orbit given AN = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*Atomic Number*([Charge-e]^2)). To calculate Radius of Bohr's Orbit, you need Quantum Number (nquantum) & Atomic Number (Z). With our tool, you need to enter the respective value for Quantum Number & Atomic 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 Radius of Orbit given AN?
In this formula, Radius of Orbit given AN uses Quantum Number & Atomic Number. We can use 2 other way(s) to calculate the same, which is/are as follows -
  • Radius of Orbit given AN = ((0.529/10000000000)*(Quantum Number^2))/Atomic Number
  • Radius of Orbit given AN = ((0.529/10000000000)*(Quantum Number^2))/Atomic Number
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