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Van der Waals Interaction Energy between Two Spherical Bodies Formula

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Van der Waals interaction energy include attraction and repulsions between atoms, molecules, and surfaces, as well as other intermolecular forces. Check FAQs

U VWaals = (- (\frac{A}{6})) \cdot ((\frac{2 \cdot R 1 \cdot R 2}{(z^{2}) - ({(R 1 + R 2)}^{2})}) + (\frac{2 \cdot R 1 \cdot R 2}{(z^{2}) - ({(R 1 - R 2)}^{2})}) + \ln (\frac{(z^{2}) - ({(R 1 + R 2)}^{2})}{(z^{2}) - ({(R 1 - R 2)}^{2})}))

U_VWaals - Van der Waals interaction energy?A - Hamaker Coefficient?R₁ - Radius of Spherical Body 1?R₂ - Radius of Spherical Body 2?z - Center-to-center Distance?

Van der Waals Interaction Energy between Two Spherical Bodies Example

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Here is how the Van der Waals Interaction Energy between Two Spherical Bodies equation looks like with Values.

Here is how the Van der Waals Interaction Energy between Two Spherical Bodies equation looks like with Units.

Here is how the Van der Waals Interaction Energy between Two Spherical Bodies equation looks like.

-0.6186 = (- (\frac{100}{6})) \cdot ((\frac{2 \cdot 12 \cdot 15}{(40^{2}) - ({(12 + 15)}^{2})}) + (\frac{2 \cdot 12 \cdot 15}{(40^{2}) - ({(12 - 15)}^{2})}) + \ln (\frac{(40^{2}) - ({(12 + 15)}^{2})}{(40^{2}) - ({(12 - 15)}^{2})}))

-0.6186J = (- (\frac{100J}{6})) \cdot ((\frac{2 \cdot 12A \cdot 15A}{({40A}^{2}) - ({(12A + 15A)}^{2})}) + (\frac{2 \cdot 12A \cdot 15A}{({40A}^{2}) - ({(12A - 15A)}^{2})}) + \ln (\frac{({40A}^{2}) - ({(12A + 15A)}^{2})}{({40A}^{2}) - ({(12A - 15A)}^{2})}))

-0.6186 = (- (\frac{100}{6})) \cdot ((\frac{2 \cdot 12 \cdot 15}{(40^{2}) - ({(12 + 15)}^{2})}) + (\frac{2 \cdot 12 \cdot 15}{(40^{2}) - ({(12 - 15)}^{2})}) + \ln (\frac{(40^{2}) - ({(12 + 15)}^{2})}{(40^{2}) - ({(12 - 15)}^{2})}))

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Van der Waals Interaction Energy between Two Spherical Bodies Solution

Follow our step by step solution on how to calculate Van der Waals Interaction Energy between Two Spherical Bodies?

FIRST Step Consider the formula

U VWaals = (- (\frac{A}{6})) \cdot ((\frac{2 \cdot R 1 \cdot R 2}{(z^{2}) - ({(R 1 + R 2)}^{2})}) + (\frac{2 \cdot R 1 \cdot R 2}{(z^{2}) - ({(R 1 - R 2)}^{2})}) + \ln (\frac{(z^{2}) - ({(R 1 + R 2)}^{2})}{(z^{2}) - ({(R 1 - R 2)}^{2})}))

Next Step Substitute values of Variables

∴

U VWaals = (- (\frac{100J}{6})) \cdot ((\frac{2 \cdot 12A \cdot 15A}{({40A}^{2}) - ({(12A + 15A)}^{2})}) + (\frac{2 \cdot 12A \cdot 15A}{({40A}^{2}) - ({(12A - 15A)}^{2})}) + \ln (\frac{({40A}^{2}) - ({(12A + 15A)}^{2})}{({40A}^{2}) - ({(12A - 15A)}^{2})}))

Next Step Convert Units

∴

U VWaals = (- (\frac{100J}{6})) \cdot ((\frac{2 \cdot 1.2E-9m \cdot 1.5E-9m}{({4E-9m}^{2}) - ({(1.2E-9m + 1.5E-9m)}^{2})}) + (\frac{2 \cdot 1.2E-9m \cdot 1.5E-9m}{({4E-9m}^{2}) - ({(1.2E-9m - 1.5E-9m)}^{2})}) + \ln (\frac{({4E-9m}^{2}) - ({(1.2E-9m + 1.5E-9m)}^{2})}{({4E-9m}^{2}) - ({(1.2E-9m - 1.5E-9m)}^{2})}))

Next Step Prepare to Evaluate

∴

U VWaals = (- (\frac{100}{6})) \cdot ((\frac{2 \cdot 1.2E-9 \cdot 1.5E-9}{({4E-9}^{2}) - ({(1.2E-9 + 1.5E-9)}^{2})}) + (\frac{2 \cdot 1.2E-9 \cdot 1.5E-9}{({4E-9}^{2}) - ({(1.2E-9 - 1.5E-9)}^{2})}) + \ln (\frac{({4E-9}^{2}) - ({(1.2E-9 + 1.5E-9)}^{2})}{({4E-9}^{2}) - ({(1.2E-9 - 1.5E-9)}^{2})}))

Next Step Evaluate

∴

U VWaals = -0.618579303089315J

LAST Step Rounding Answer

∴

U VWaals = -0.6186J

Van der Waals Interaction Energy between Two Spherical Bodies Formula Elements

Variables

Functions

Van der Waals interaction energy

Van der Waals interaction energy include attraction and repulsions between atoms, molecules, and surfaces, as well as other intermolecular forces.

Symbol: U_VWaals

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Van der Waals interaction energy

Hamaker Coefficient

Hamaker coefficient A can be defined for a Van der Waals body–body interaction.

Symbol: A

Measurement: EnergyUnit: J

Note: Value can be positive or negative.

Formulas to find Hamaker Coefficient

Radius of Spherical Body 1

Radius of Spherical Body 1 represented as R1.

Symbol: R₁

Measurement: LengthUnit: A

Note: Value can be positive or negative.

Formulas to find Radius of Spherical Body 1

Radius of Spherical Body 2

Radius of Spherical Body 2 represented as R1.

Symbol: R₂

Measurement: LengthUnit: A

Note: Value can be positive or negative.

Formulas to find Radius of Spherical Body 2

Center-to-center Distance

Center-to-center Distance is a concept for distances, also called on-center spacing, z = R1 + R2 + r.

Symbol: z

Measurement: LengthUnit: A

Note: Value should be greater than 0.

Formulas to find Center-to-center Distance

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other formulas in Van der Waals Force category

Go Potential Energy in Limit of Closest-Approach

PE Limit = \frac{- A \cdot R 1 \cdot R 2}{(R 1 + R 2) \cdot 6 \cdot r}

Go Distance between Surfaces given Potential Energy in Limit of Close-Approach

r = \frac{- A \cdot R 1 \cdot R 2}{(R 1 + R 2) \cdot 6 \cdot PE}

Go Radius of Spherical Body 1 given Potential Energy in Limit of Closest-Approach

R 1 = \frac{1}{(- \frac{A}{PE \cdot 6 \cdot r}) - (\frac{1}{R 2})}

Go Radius of Spherical Body 2 given Potential Energy in Limit of Closest-Approach

R 2 = \frac{1}{(- \frac{A}{PE \cdot 6 \cdot r}) - (\frac{1}{R 1})}

How to Evaluate Van der Waals Interaction Energy between Two Spherical Bodies?

Van der Waals Interaction Energy between Two Spherical Bodies evaluator uses Van der Waals interaction energy = (-(Hamaker Coefficient/6))*(((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2)))+((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))+ln(((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2))/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))) to evaluate the Van der Waals interaction energy, The Van der Waals interaction energy between two spherical bodies of radii R1 and R2 and with smooth surfaces was approximated in 1937 by Hamaker (using London's famous 1937 equation for the dispersion interaction energy between atoms/molecules as the starting point). Van der Waals interaction energy is denoted by U_VWaals symbol.

How to evaluate Van der Waals Interaction Energy between Two Spherical Bodies using this online evaluator? To use this online evaluator for Van der Waals Interaction Energy between Two Spherical Bodies, enter Hamaker Coefficient (A), Radius of Spherical Body 1 (R₁), Radius of Spherical Body 2 (R₂) & Center-to-center Distance (z) and hit the calculate button.

FAQs on Van der Waals Interaction Energy between Two Spherical Bodies

What is the formula to find Van der Waals Interaction Energy between Two Spherical Bodies?

The formula of Van der Waals Interaction Energy between Two Spherical Bodies is expressed as Van der Waals interaction energy = (-(Hamaker Coefficient/6))*(((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2)))+((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))+ln(((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2))/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))). Here is an example- -0.618579 = (-(100/6))*(((2*1.2E-09*1.5E-09)/((4E-09^2)-((1.2E-09+1.5E-09)^2)))+((2*1.2E-09*1.5E-09)/((4E-09^2)-((1.2E-09-1.5E-09)^2)))+ln(((4E-09^2)-((1.2E-09+1.5E-09)^2))/((4E-09^2)-((1.2E-09-1.5E-09)^2)))).

How to calculate Van der Waals Interaction Energy between Two Spherical Bodies?

With Hamaker Coefficient (A), Radius of Spherical Body 1 (R₁), Radius of Spherical Body 2 (R₂) & Center-to-center Distance (z) we can find Van der Waals Interaction Energy between Two Spherical Bodies using the formula - Van der Waals interaction energy = (-(Hamaker Coefficient/6))*(((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2)))+((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))+ln(((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2))/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))). This formula also uses Natural Logarithm Function function(s).

Can the Van der Waals Interaction Energy between Two Spherical Bodies be negative?

Yes, the Van der Waals Interaction Energy between Two Spherical Bodies, measured in Energy can be negative.

Which unit is used to measure Van der Waals Interaction Energy between Two Spherical Bodies?

Van der Waals Interaction Energy between Two Spherical Bodies is usually measured using the Joule[J] for Energy. Kilojoule[J], Gigajoule[J], Megajoule[J] are the few other units in which Van der Waals Interaction Energy between Two Spherical Bodies can be measured.

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Van der Waals Interaction Energy between Two Spherical Bodies Formula

Van der Waals Interaction Energy between Two Spherical Bodies Example

Van der Waals Interaction Energy between Two Spherical Bodies Solution

Van der Waals Interaction Energy between Two Spherical Bodies Formula Elements

Other formulas in Van der Waals Force category

How to Evaluate Van der Waals Interaction Energy between Two Spherical Bodies?

FAQs on Van der Waals Interaction Energy between Two Spherical Bodies

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