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

Formula Used:

\[ R1 = \frac{1}{\left(-\frac{A}{PE \times 6 \times r}\right) - \frac{1}{R2}} \]

Hamaker Coefficient (A):

Joule

Potential Energy (PE):

Joule

Distance Between Surfaces (r):

Meter

Radius of Spherical Body 2 (R2):

Meter

Radius of Spherical Body 1 (R1):

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1. What is Radius of Spherical Body 1?

The Radius of Spherical Body 1 is a key parameter in calculating Van der Waals interactions between two spherical bodies. It represents the size of the first spherical particle in the interaction system.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R1 = \frac{1}{\left(-\frac{A}{PE \times 6 \times r}\right) - \frac{1}{R2}} \]

Where:

\( R1 \) — Radius of Spherical Body 1 (Meter)
\( A \) — Hamaker Coefficient (Joule)
\( PE \) — Potential Energy (Joule)
\( r \) — Distance Between Surfaces (Meter)
\( R2 \) — Radius of Spherical Body 2 (Meter)

Explanation: This formula calculates the radius of the first spherical body based on the given potential energy and other interaction parameters in the limit of closest approach.

3. Importance of Calculation

Details: Accurate calculation of spherical body radius is crucial for understanding Van der Waals interactions, colloidal stability, and surface forces in various physical and chemical systems.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure Hamaker Coefficient, Potential Energy, Distance Between Surfaces, and Radius of Spherical Body 2 are non-zero values for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the Hamaker Coefficient?
A: The Hamaker coefficient is a constant that describes the magnitude of Van der Waals forces between materials.

Q2: What does negative potential energy indicate?
A: Negative potential energy typically indicates an attractive interaction between the spherical bodies.

Q3: How does distance affect the calculation?
A: The interaction strength decreases with increasing distance between the surfaces, following an inverse relationship.

Q4: What are typical values for spherical body radii?
A: Radii can range from nanometers for colloidal particles to micrometers for larger particles, depending on the specific system.

Q5: When is this calculation most applicable?
A: This calculation is particularly useful in colloidal science, surface chemistry, and nanotechnology applications where Van der Waals interactions dominate.