Bond Length of Diatomic Molecule in Rotational Spectrum Calculator

✖Wave Number in Spectroscopy, it is customary to represent energy in wavenumbers.ⓘ Wave Number in Spectroscopy [B~]			+10% -10%
✖The Reduced Mass is the "effective" inertial mass appearing in the two-body problem. It is a quantity which allows the two-body problem to be solved as if it were a one-body problem.ⓘ Reduced Mass [μ]			+10% -10%

✖Bond Length of Diatomic Molecule is the distance between center of two molecules(or two masses).ⓘ Bond Length of Diatomic Molecule in Rotational Spectrum [L_{bond_d}]

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Formula

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Bond Length of Diatomic Molecule in Rotational Spectrum

Formula

`"L"_{"bond_d"} = sqrt("[hP]"/(8*(pi^2)*"[c]"*"B~"*"μ"))`

Example

`"1.2E^-22cm"=sqrt("[hP]"/(8*(pi^2)*"[c]"*"2500/m"*"8kg"))`

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Bond Length of Diatomic Molecule in Rotational Spectrum Solution

STEP 0: Pre-Calculation Summary

Formula Used

Bond Length of Diatomic Molecule = sqrt([hP]/(8*(pi^2)*[c]*Wave Number in Spectroscopy*Reduced Mass))
L_{bond_d} = sqrt([hP]/(8*(pi^2)*[c]*B~*μ))
This formula uses 3 Constants, 1 Functions, 3 Variables

Constants Used

[hP] - Planck constant Value Taken As 6.626070040E-34
[c] - Light speed in vacuum Value Taken As 299792458.0
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Bond Length of Diatomic Molecule - (Measured in Meter) - Bond Length of Diatomic Molecule is the distance between center of two molecules(or two masses).
Wave Number in Spectroscopy - (Measured in Diopter) - Wave Number in Spectroscopy, it is customary to represent energy in wavenumbers.
Reduced Mass - (Measured in Kilogram) - The Reduced Mass is the "effective" inertial mass appearing in the two-body problem. It is a quantity which allows the two-body problem to be solved as if it were a one-body problem.

STEP 1: Convert Input(s) to Base Unit

Wave Number in Spectroscopy: 2500 1 per Meter --> 2500 Diopter (Check conversion here)
Reduced Mass: 8 Kilogram --> 8 Kilogram No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_{bond_d} = sqrt([hP]/(8*(pi^2)*[c]*B~*μ)) --> sqrt([hP]/(8*(pi^2)*[c]*2500*8))

Evaluating ... ...

L_{bond_d} = 1.18306279161896E-24

STEP 3: Convert Result to Output's Unit

1.18306279161896E-24 Meter -->1.18306279161896E-22 Centimeter (Check conversion here)

FINAL ANSWER

1.18306279161896E-22 ≈ 1.2E-22 Centimeter <-- Bond Length of Diatomic Molecule

(Calculation completed in 00.004 seconds)

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Created by Nishant Sihag

Indian Institute of Technology (IIT), Delhi

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Verified by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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< 8 Bond Length Calculators

Bond Length given Moment of Inertia

Go Bond Length given Moment of Inertia2 = sqrt(Moment of Inertia*((Mass 1+Mass 2)/(Mass 1*Mass 2)))

Bond Length of Diatomic Molecule in Rotational Spectrum

Go Bond Length of Diatomic Molecule = sqrt([hP]/(8*(pi^2)*[c]*Wave Number in Spectroscopy*Reduced Mass))

Bond Length given Masses and Radius 1

Go Bond Length given Masses and Radius 1 = (Mass 1+Mass 2)*Radius of Mass 1/Mass 2

Bond Length given Masses and Radius 2

Go Bond Length = Radius of Mass 2*(Mass 1+Mass 2)/Mass 1

Bond Length given Reduced Mass

Go Bond Length given Moment of Inertia2 = sqrt(Moment of Inertia/Reduced Mass)

Radius 1 of Rotation given Bond Length

Go Radius of Mass 1 = Bond Length-Radius of Mass 2

Radius 2 of Rotation given Bond Length

Go Radius of Mass 2 = Bond Length-Radius of Mass 1

Bond Length

Go Bond Length = Radius of Mass 1+Radius of Mass 2

< 8 Bond length Calculators

Bond Length given Moment of Inertia

Go Bond Length given Moment of Inertia2 = sqrt(Moment of Inertia*((Mass 1+Mass 2)/(Mass 1*Mass 2)))

Bond Length of Diatomic Molecule in Rotational Spectrum

Go Bond Length of Diatomic Molecule = sqrt([hP]/(8*(pi^2)*[c]*Wave Number in Spectroscopy*Reduced Mass))

Bond Length given Masses and Radius 1

Go Bond Length given Masses and Radius 1 = (Mass 1+Mass 2)*Radius of Mass 1/Mass 2

Bond Length given Masses and Radius 2

Go Bond Length = Radius of Mass 2*(Mass 1+Mass 2)/Mass 1

Bond Length given Reduced Mass

Go Bond Length given Moment of Inertia2 = sqrt(Moment of Inertia/Reduced Mass)

Radius 1 of Rotation given Bond Length

Go Radius of Mass 1 = Bond Length-Radius of Mass 2

Radius 2 of Rotation given Bond Length

Go Radius of Mass 2 = Bond Length-Radius of Mass 1

Bond Length

Go Bond Length = Radius of Mass 1+Radius of Mass 2

Bond Length of Diatomic Molecule in Rotational Spectrum Formula

Bond Length of Diatomic Molecule = sqrt([hP]/(8*(pi^2)*[c]*Wave Number in Spectroscopy*Reduced Mass))
L_{bond_d} = sqrt([hP]/(8*(pi^2)*[c]*B~*μ))

Do we have some selection rules?

Yes, Selection rules only permit transitions between consecutive rotational levels: ΔJ=J±1 , and require the molecule to contain a permanent dipole moment. Due to the dipole requirement, molecules such as HF and HCl have pure rotational spectra and molecules such as H2 and N2 are rotationally inactive.

How to Calculate Bond Length of Diatomic Molecule in Rotational Spectrum?

Bond Length of Diatomic Molecule in Rotational Spectrum calculator uses Bond Length of Diatomic Molecule = sqrt([hP]/(8*(pi^2)*[c]*Wave Number in Spectroscopy*Reduced Mass)) to calculate the Bond Length of Diatomic Molecule, The Bond length of diatomic molecule in rotational spectrum formula is defined as contrasts vibrational spectra which have only one fundamental peak for each vibrational mode. From the rotational spectrum of a diatomic molecule the bond length can be determined. Because B~ is a function of I and therefore a function of l (bond length). Bond Length of Diatomic Molecule is denoted by L_{bond_d} symbol.

How to calculate Bond Length of Diatomic Molecule in Rotational Spectrum using this online calculator? To use this online calculator for Bond Length of Diatomic Molecule in Rotational Spectrum, enter Wave Number in Spectroscopy (B~) & Reduced Mass (μ) and hit the calculate button. Here is how the Bond Length of Diatomic Molecule in Rotational Spectrum calculation can be explained with given input values -> 1.2E-20 = sqrt([hP]/(8*(pi^2)*[c]*2500*8)).

FAQ

What is Bond Length of Diatomic Molecule in Rotational Spectrum?

The Bond length of diatomic molecule in rotational spectrum formula is defined as contrasts vibrational spectra which have only one fundamental peak for each vibrational mode. From the rotational spectrum of a diatomic molecule the bond length can be determined. Because B~ is a function of I and therefore a function of l (bond length) and is represented as L_{bond_d} = sqrt([hP]/(8*(pi^2)*[c]*B~*μ)) or Bond Length of Diatomic Molecule = sqrt([hP]/(8*(pi^2)*[c]*Wave Number in Spectroscopy*Reduced Mass)). Wave Number in Spectroscopy, it is customary to represent energy in wavenumbers & The Reduced Mass is the "effective" inertial mass appearing in the two-body problem. It is a quantity which allows the two-body problem to be solved as if it were a one-body problem.

How to calculate Bond Length of Diatomic Molecule in Rotational Spectrum?

The Bond length of diatomic molecule in rotational spectrum formula is defined as contrasts vibrational spectra which have only one fundamental peak for each vibrational mode. From the rotational spectrum of a diatomic molecule the bond length can be determined. Because B~ is a function of I and therefore a function of l (bond length) is calculated using Bond Length of Diatomic Molecule = sqrt([hP]/(8*(pi^2)*[c]*Wave Number in Spectroscopy*Reduced Mass)). To calculate Bond Length of Diatomic Molecule in Rotational Spectrum, you need Wave Number in Spectroscopy (B~) & Reduced Mass (μ). With our tool, you need to enter the respective value for Wave Number in Spectroscopy & Reduced Mass and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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