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Radius of Bohr's Orbit Calculator

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Radius of Bohr's Orbit Electrons and Orbits Hydrogen Spectrum

✖Quantum Number describe values of conserved quantities in the dynamics of a quantum system.ⓘ Quantum Number [n_quantum]			+10% -10%
✖Atomic Number is the number of protons present inside the nucleus of an atom of an element.ⓘ Atomic Number [Z]			+10% -10%

✖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 [r_{orbit_AN}]

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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))
r_{orbit_AN} = ((n_quantum^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

r_{orbit_AN} = ((n_quantum^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 ... ...

r_{orbit_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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Created by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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Indian Institute of Technology (IIT), Kanpur

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< Radius of Bohr's Orbit Calculators

Radius of Bohr's Orbit

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

Radius of Bohr's Orbit for Hydrogen Atom

LaTeX Go Radius of Orbit given AV = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2))

Radius of Bohr's Orbit given Atomic Number

LaTeX Go Radius of Orbit given AN = ((0.529/10000000000)*(Quantum Number^2))/Atomic Number

Radius of Orbit given Angular Velocity

LaTeX Go Radius of Orbit given AV = Velocity of Electron/Angular Velocity

< Important Formulas on Bohr's Atomic Model Calculators

Change in Wave Number of Moving Particle

LaTeX 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))

Atomic Mass

LaTeX Go Atomic Mass = Total Mass of Proton+Total Mass of Neutron

Number of Electrons in nth Shell

LaTeX Go Number of Electrons in nth Shell = (2*(Quantum Number^2))

Orbital Frequency of Electron

LaTeX Go Orbital Frequency = 1/Time Period of Electron

Radius of Bohr's Orbit Formula

LaTeX Go

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 r_{orbit_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 (n_quantum) & 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 r_{orbit_AN} = ((n_quantum^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 (n_quantum) & 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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