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

✖Hamaker coefficient A can be defined for a Van der Waals body–body interaction.ⓘ Hamaker Coefficient [A]			+10% -10%
✖Potential Energy is the energy that is stored in an object due to its position relative to some zero position.ⓘ Potential Energy [PE]			+10% -10%
✖Distance between surfaces is the length of the line segment between the 2 surfaces.ⓘ Distance Between Surfaces [r]			+10% -10%
✖Radius of Spherical Body 2 represented as R1.ⓘ Radius of Spherical Body 2 [R₂]			+10% -10%

✖Radius of Spherical Body 1 represented as R1.ⓘ Radius of Spherical Body 1 given Potential Energy in Limit of Closest-Approach [R₁]

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Formula

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

Formula

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

Example

-2.068966 A = \frac{1}{(- \frac{100 J}{4 J \cdot 6 \cdot 10 A}) - (\frac{1}{15 A})}

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

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Spherical Body 1 = 1/((-Hamaker Coefficient/(Potential Energy*6*Distance Between Surfaces))-(1/Radius of Spherical Body 2))
R₁ = 1/((-A/(PE*6*r))-(1/R₂))
This formula uses 5 Variables

Variables Used

Radius of Spherical Body 1 - (Measured in Meter) - Radius of Spherical Body 1 represented as R1.
Hamaker Coefficient - (Measured in Joule) - Hamaker coefficient A can be defined for a Van der Waals body–body interaction.
Potential Energy - (Measured in Joule) - Potential Energy is the energy that is stored in an object due to its position relative to some zero position.
Distance Between Surfaces - (Measured in Meter) - Distance between surfaces is the length of the line segment between the 2 surfaces.
Radius of Spherical Body 2 - (Measured in Meter) - Radius of Spherical Body 2 represented as R1.

STEP 1: Convert Input(s) to Base Unit

Hamaker Coefficient: 100 Joule --> 100 Joule No Conversion Required
Potential Energy: 4 Joule --> 4 Joule No Conversion Required
Distance Between Surfaces: 10 Angstrom --> 1E-09 Meter (Check conversion here)
Radius of Spherical Body 2: 15 Angstrom --> 1.5E-09 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R₁ = 1/((-A/(PE*6*r))-(1/R₂)) --> 1/((-100/(4*6*1E-09))-(1/1.5E-09))

Evaluating ... ...

R₁ = -2.06896551724138E-10

STEP 3: Convert Result to Output's Unit

-2.06896551724138E-10 Meter -->-2.06896551724138 Angstrom (Check conversion here)

FINAL ANSWER

-2.06896551724138 ≈ -2.068966 Angstrom <-- Radius of Spherical Body 1

(Calculation completed in 00.004 seconds)

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< Van der Waals Force Calculators

Van der Waals Interaction Energy between Two Spherical Bodies

Go 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))))

Potential Energy in Limit of Closest-Approach

Go Potential Energy In Limit = (-Hamaker Coefficient*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Radius of Spherical Body 1+Radius of Spherical Body 2)*6*Distance Between Surfaces)

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

Go Distance Between Surfaces = (-Hamaker Coefficient*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Radius of Spherical Body 1+Radius of Spherical Body 2)*6*Potential Energy)

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

Go Radius of Spherical Body 1 = 1/((-Hamaker Coefficient/(Potential Energy*6*Distance Between Surfaces))-(1/Radius of Spherical Body 2))

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

Radius of Spherical Body 1 = 1/((-Hamaker Coefficient/(Potential Energy*6*Distance Between Surfaces))-(1/Radius of Spherical Body 2))
R₁ = 1/((-A/(PE*6*r))-(1/R₂))

What are main characteristics of Van der Waals forces?

1) They are weaker than normal covalent and ionic bonds.
2) Van der Waals forces are additive and cannot be saturated.
3) They have no directional characteristic.
4) They are all short-range forces and hence only interactions between the nearest particles need to be considered (instead of all the particles). Van der Waals attraction is greater if the molecules are closer.
5) Van der Waals forces are independent of temperature except for dipole – dipole interactions.

How to Calculate Radius of Spherical Body 1 given Potential Energy in Limit of Closest-Approach?

Radius of Spherical Body 1 given Potential Energy in Limit of Closest-Approach calculator uses Radius of Spherical Body 1 = 1/((-Hamaker Coefficient/(Potential Energy*6*Distance Between Surfaces))-(1/Radius of Spherical Body 2)) to calculate the Radius of Spherical Body 1, The Radius of spherical body 1 given Potential Energy in limit of closest-approach formula is the radius of spherical body 1 represented as R1. Radius of Spherical Body 1 is denoted by R₁ symbol.

How to calculate Radius of Spherical Body 1 given Potential Energy in Limit of Closest-Approach using this online calculator? To use this online calculator for Radius of Spherical Body 1 given Potential Energy in Limit of Closest-Approach, enter Hamaker Coefficient (A), Potential Energy (PE), Distance Between Surfaces (r) & Radius of Spherical Body 2 (R₂) and hit the calculate button. Here is how the Radius of Spherical Body 1 given Potential Energy in Limit of Closest-Approach calculation can be explained with given input values -> -20689655172.4138 = 1/((-100/(4*6*1E-09))-(1/1.5E-09)).

FAQ

What is Radius of Spherical Body 1 given Potential Energy in Limit of Closest-Approach?

The Radius of spherical body 1 given Potential Energy in limit of closest-approach formula is the radius of spherical body 1 represented as R1 and is represented as R₁ = 1/((-A/(PE*6*r))-(1/R₂)) or Radius of Spherical Body 1 = 1/((-Hamaker Coefficient/(Potential Energy*6*Distance Between Surfaces))-(1/Radius of Spherical Body 2)). Hamaker coefficient A can be defined for a Van der Waals body–body interaction, Potential Energy is the energy that is stored in an object due to its position relative to some zero position, Distance between surfaces is the length of the line segment between the 2 surfaces & Radius of Spherical Body 2 represented as R1.

How to calculate Radius of Spherical Body 1 given Potential Energy in Limit of Closest-Approach?

The Radius of spherical body 1 given Potential Energy in limit of closest-approach formula is the radius of spherical body 1 represented as R1 is calculated using Radius of Spherical Body 1 = 1/((-Hamaker Coefficient/(Potential Energy*6*Distance Between Surfaces))-(1/Radius of Spherical Body 2)). To calculate Radius of Spherical Body 1 given Potential Energy in Limit of Closest-Approach, you need Hamaker Coefficient (A), Potential Energy (PE), Distance Between Surfaces (r) & Radius of Spherical Body 2 (R₂). With our tool, you need to enter the respective value for Hamaker Coefficient, Potential Energy, Distance Between Surfaces & Radius of Spherical Body 2 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 Spherical Body 1?

In this formula, Radius of Spherical Body 1 uses Hamaker Coefficient, Potential Energy, Distance Between Surfaces & Radius of Spherical Body 2. We can use 2 other way(s) to calculate the same, which is/are as follows -

Radius of Spherical Body 1 = 1/((Hamaker Coefficient/(Van der Waals force*6*(Distance Between Surfaces^2)))-(1/Radius of Spherical Body 2))
Radius of Spherical Body 1 = Center-to-center Distance-Distance Between Surfaces-Radius of Spherical Body 2

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