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Radius of Bohr's orbit for the Hydrogen atom Solution

STEP 0: Pre-Calculation Summary
Formula Used
radius_of_orbit = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2))
r = ((n^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2))
This formula uses 6 Constants, 1 Functions, 1 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
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
[Coulomb] - Coulomb constant Value Taken As 9E9
Functions Used
C - Binomial coefficient function, C(n,k)
Variables Used
Quantum Number- Quantum Number describe values of conserved quantities in the dynamics of a quantum system.
STEP 1: Convert Input(s) to Base Unit
Quantum Number: 1 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
r = ((n^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2)) --> ((1^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2))
Evaluating ... ...
r = 5.28445287709678E-11
STEP 3: Convert Result to Output's Unit
5.28445287709678E-11 Meter -->0.528445287709678 Angstrom (Check conversion here)
FINAL ANSWER
0.528445287709678 Angstrom <-- Radius of orbit
(Calculation completed in 00.000 seconds)

10+ Bohr's atomic model Calculators

Radius of Bohr's orbit
radius_of_orbit = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*Atomic number*([Charge-e]^2)) Go
Total energy of electron in nth orbit
energy = (-([Mass-e]*([Charge-e]^4)*(Atomic number^2))/(8*([Permitivity-vacuum]^2)*(Quantum Number^2)*([hP]^2))) Go
Radius of Bohr's orbit for the Hydrogen atom
radius_of_orbit = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2)) Go
Velocity of electron in Bohr's orbit
velocity_of_electron = ([Charge-e]^2)/(2*[Permitivity-vacuum]*Quantum Number*[hP]) Go
Ionization potential
ionization_potential = ([Rydberg]*(Atomic number^2))/(Quantum Number^2) Go
Velocity of electron when time period of electron is given
velocity_of_electron = (2*pi*Radius of orbit)/Time period of electron Go
Radius of Bohr's orbit when atomic number is given
radius_of_orbit = (0.529*(Quantum Number^2))/Atomic number Go
Velocity of electron in orbit when angular velocity is given
velocity_of_electron = Angular Velocity*Radius of orbit Go
Radius of orbit when angular velocity is given
radius_of_orbit = Velocity of electron/Angular Velocity Go
Wave number when frequency of photon is given
wave_number_of_particle = Frequency of photon/[c] Go

Radius of Bohr's orbit for the Hydrogen atom Formula

radius_of_orbit = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2))
r = ((n^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([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 for the Hydrogen atom?

Radius of Bohr's orbit for the Hydrogen atom calculator uses radius_of_orbit = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2)) to calculate the Radius of orbit, The Radius of Bohr's orbit for the Hydrogen atom is defined as a physical constant, expressing the most probable distance between the electron and the nucleus in a Hydrogen atom(Z=1). Radius of orbit and is denoted by r symbol.

How to calculate Radius of Bohr's orbit for the Hydrogen atom using this online calculator? To use this online calculator for Radius of Bohr's orbit for the Hydrogen atom, enter Quantum Number (n) and hit the calculate button. Here is how the Radius of Bohr's orbit for the Hydrogen atom calculation can be explained with given input values -> 0.528445 = ((1^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2)).

FAQ

What is Radius of Bohr's orbit for the Hydrogen atom?
The Radius of Bohr's orbit for the Hydrogen atom is defined as a physical constant, expressing the most probable distance between the electron and the nucleus in a Hydrogen atom(Z=1) and is represented as r = ((n^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2)) or radius_of_orbit = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2)). Quantum Number describe values of conserved quantities in the dynamics of a quantum system.
How to calculate Radius of Bohr's orbit for the Hydrogen atom?
The Radius of Bohr's orbit for the Hydrogen atom is defined as a physical constant, expressing the most probable distance between the electron and the nucleus in a Hydrogen atom(Z=1) is calculated using radius_of_orbit = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2)). To calculate Radius of Bohr's orbit for the Hydrogen atom, you need Quantum Number (n). With our tool, you need to enter the respective value for 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 Radius of orbit?
In this formula, Radius of orbit uses Quantum Number. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • velocity_of_electron = Angular Velocity*Radius of orbit
  • radius_of_orbit = Velocity of electron/Angular Velocity
  • radius_of_orbit = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*Atomic number*([Charge-e]^2))
  • radius_of_orbit = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2))
  • energy = (-([Mass-e]*([Charge-e]^4)*(Atomic number^2))/(8*([Permitivity-vacuum]^2)*(Quantum Number^2)*([hP]^2)))
  • wave_number_of_particle = Frequency of photon/[c]
  • ionization_potential = ([Rydberg]*(Atomic number^2))/(Quantum Number^2)
  • velocity_of_electron = (2*pi*Radius of orbit)/Time period of electron
  • radius_of_orbit = (0.529*(Quantum Number^2))/Atomic number
  • velocity_of_electron = ([Charge-e]^2)/(2*[Permitivity-vacuum]*Quantum Number*[hP])
Where is the Radius of Bohr's orbit for the Hydrogen atom calculator used?
Among many, Radius of Bohr's orbit for the Hydrogen atom calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}
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