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Radius of Bohr's Orbit for Hydrogen Atom Formula

GoRadius of Orbit given Angular Velocity Formula

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Radius of Orbit given AV is the distance from the center of orbit of an electron to a point on its surface. Check FAQs

r orbit_AV = \frac{({n quantum}^{2}) \cdot ({[hP]}^{2})}{4 \cdot (π^{2}) \cdot [Mass-e] \cdot [Coulomb] \cdot ({[Charge-e]}^{2})}

r_{orbit_AV} - Radius of Orbit given AV?n_quantum - Quantum Number?[hP] - Planck constant?[Mass-e] - Mass of electron?[Coulomb] - Coulomb constant?[Charge-e] - Charge of electron?π - Archimedes' constant?

Radius of Bohr's Orbit for Hydrogen Atom Example

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Here is how the Radius of Bohr's Orbit for Hydrogen Atom equation looks like with Values.

Here is how the Radius of Bohr's Orbit for Hydrogen Atom equation looks like with Units.

Here is how the Radius of Bohr's Orbit for Hydrogen Atom equation looks like.

3.3867 = \frac{(8^{2}) \cdot ({6.6E-34}^{2})}{4 \cdot ({3.1416}^{2}) \cdot 9.1E-31 \cdot 9E+9 \cdot ({1.6E-19}^{2})}

3.3867nm = \frac{(8^{2}) \cdot ({6.6E-34}^{2})}{4 \cdot ({3.1416}^{2}) \cdot 9.1E-31kg \cdot 9E+9 \cdot ({1.6E-19C}^{2})}

3.3867 = \frac{(8^{2}) \cdot ({6.6E-34}^{2})}{4 \cdot ({3.1416}^{2}) \cdot 9.1E-31 \cdot 9E+9 \cdot ({1.6E-19}^{2})}

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Bohr's Atomic Model » fx Radius of Bohr's Orbit for Hydrogen Atom

Radius of Bohr's Orbit for Hydrogen Atom Solution

Follow our step by step solution on how to calculate Radius of Bohr's Orbit for Hydrogen Atom?

FIRST Step Consider the formula

r orbit_AV = \frac{({n quantum}^{2}) \cdot ({[hP]}^{2})}{4 \cdot (π^{2}) \cdot [Mass-e] \cdot [Coulomb] \cdot ({[Charge-e]}^{2})}

Next Step Substitute values of Variables

∴

r orbit_AV = \frac{(8^{2}) \cdot ({[hP]}^{2})}{4 \cdot (π^{2}) \cdot [Mass-e] \cdot [Coulomb] \cdot ({[Charge-e]}^{2})}

Next Step Substitute values of Constants

∴

r orbit_AV = \frac{(8^{2}) \cdot ({6.6E-34}^{2})}{4 \cdot ({3.1416}^{2}) \cdot 9.1E-31kg \cdot 9E+9 \cdot ({1.6E-19C}^{2})}

Next Step Prepare to Evaluate

∴

r orbit_AV = \frac{(8^{2}) \cdot ({6.6E-34}^{2})}{4 \cdot ({3.1416}^{2}) \cdot 9.1E-31 \cdot 9E+9 \cdot ({1.6E-19}^{2})}

Next Step Evaluate

∴

r orbit_AV = 3.38673414913228E-09m

Next Step Convert to Output's Unit

∴

r orbit_AV = 3.38673414913228nm

LAST Step Rounding Answer

∴

r orbit_AV = 3.3867nm

Radius of Bohr's Orbit for Hydrogen Atom Formula Elements

Variables

Constants

Radius of Orbit given AV

Radius of Orbit given AV is the distance from the center of orbit of an electron to a point on its surface.

Symbol: r_{orbit_AV}

Measurement: LengthUnit: nm

Note: Value can be positive or negative.

Formulas to find Radius of Orbit given AV

Quantum Number

Quantum Number describe values of conserved quantities in the dynamics of a quantum system.

Symbol: n_quantum

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Quantum Number

Planck constant

Planck constant is a fundamental universal constant that defines the quantum nature of energy and relates the energy of a photon to its frequency.

Symbol: [hP]

Value: 6.626070040E-34

Mass of electron

Mass of electron is a fundamental physical constant, representing the amount of matter contained within an electron, an elementary particle with a negative electric charge.

Symbol: [Mass-e]

Value: 9.10938356E-31 kg

Coulomb constant

Coulomb constant appears in Coulomb's law and quantifies the electrostatic force between two point charges. It plays a fundamental role in the study of electrostatics.

Symbol: [Coulomb]

Value: 8.9875E+9

Charge of electron

Charge of electron is a fundamental physical constant, representing the electric charge carried by an electron, which is the elementary particle with a negative electric charge.

Symbol: [Charge-e]

Value: 1.60217662E-19 C

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Radius of Orbit given AV

Go Radius of Orbit given Angular Velocity

r orbit_AV = \frac{v e}{ω}

Other formulas in Radius of Bohr's Orbit category

Go Radius of Bohr's Orbit

r orbit_AN = \frac{({n quantum}^{2}) \cdot ({[hP]}^{2})}{4 \cdot (π^{2}) \cdot [Mass-e] \cdot [Coulomb] \cdot Z \cdot ({[Charge-e]}^{2})}

Go Radius of Bohr's Orbit given Atomic Number

r orbit_AN = \frac{(\frac{0.529}{10000000000}) \cdot ({n quantum}^{2})}{Z}

Go Radius of Orbit

r o = \frac{n quantum \cdot [hP]}{2 \cdot π \cdot Mass flight path \cdot v}

Go Bohr's Radius

a o = (\frac{n quantum}{Z}) \cdot 0.529 \cdot 10^{- 10}

How to Evaluate Radius of Bohr's Orbit for Hydrogen Atom?

Radius of Bohr's Orbit for Hydrogen Atom evaluator uses Radius of Orbit given AV = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2)) to evaluate the Radius of Orbit given AV, The Radius of Bohr's Orbit for 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 given AV is denoted by r_{orbit_AV} symbol.

How to evaluate Radius of Bohr's Orbit for Hydrogen Atom using this online evaluator? To use this online evaluator for Radius of Bohr's Orbit for Hydrogen Atom, enter Quantum Number (n_quantum) and hit the calculate button.

FAQs on Radius of Bohr's Orbit for Hydrogen Atom

What is the formula to find Radius of Bohr's Orbit for Hydrogen Atom?

The formula of Radius of Bohr's Orbit for Hydrogen Atom is expressed as Radius of Orbit given AV = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2)). Here is an example- 3.4E+9 = ((8^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2)).

How to calculate Radius of Bohr's Orbit for Hydrogen Atom?

With Quantum Number (n_quantum) we can find Radius of Bohr's Orbit for Hydrogen Atom using the formula - Radius of Orbit given AV = ((Quantum Number^2)*([hP]^2))/(4*(pi^2)*[Mass-e]*[Coulomb]*([Charge-e]^2)). This formula also uses Planck constant, Mass of electron, Coulomb constant, Charge of electron, Archimedes' constant .

What are the other ways to Calculate Radius of Orbit given AV?

Here are the different ways to Calculate Radius of Orbit given AV-

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

Can the Radius of Bohr's Orbit for Hydrogen Atom be negative?

Yes, the Radius of Bohr's Orbit for Hydrogen Atom, measured in Length can be negative.

Which unit is used to measure Radius of Bohr's Orbit for Hydrogen Atom?

Radius of Bohr's Orbit for Hydrogen Atom is usually measured using the Nanometer[nm] for Length. Meter[nm], Millimeter[nm], Kilometer[nm] are the few other units in which Radius of Bohr's Orbit for Hydrogen Atom can be measured.

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