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

Formula Used:

\[ R_2 = \frac{1}{\left(-\frac{A}{PE \cdot 6 \cdot r}\right) - \frac{1}{R_1}} \]

Hamaker Coefficient (A):

Potential Energy (PE):

Distance Between Surfaces (r):

Radius of Spherical Body 1 (R1):

Radius of Spherical Body 2 (R2):

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1. What is the Radius of Spherical Body 2 Calculation?

This calculator determines the radius of a second spherical body (R2) based on the Van der Waals interaction potential energy between two spherical bodies at their closest approach distance. The calculation uses the Hamaker coefficient, potential energy, distance between surfaces, and the radius of the first spherical body.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R_2 = \frac{1}{\left(-\frac{A}{PE \cdot 6 \cdot r}\right) - \frac{1}{R_1}} \]

Where:

\( R_2 \) — Radius of Spherical Body 2 (m)
\( A \) — Hamaker Coefficient (J)
\( PE \) — Potential Energy (J)
\( r \) — Distance Between Surfaces (m)
\( R_1 \) — Radius of Spherical Body 1 (m)

Explanation: This formula calculates the radius of the second spherical body based on the interaction potential energy between two spherical bodies at their closest approach distance, considering the Van der Waals forces described by the Hamaker coefficient.

3. Importance of This Calculation

Details: This calculation is important in colloidal science, surface chemistry, and nanotechnology for understanding the interaction forces between spherical particles and predicting their behavior in various environments.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure all input values are positive and non-zero for accurate calculation results.

5. Frequently Asked Questions (FAQ)

Q1: What is the Hamaker coefficient?
A: The Hamaker coefficient is a constant that describes the magnitude of the Van der Waals force between two bodies.

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

Q3: Can this formula be used for any spherical bodies?
A: This formula is specifically designed for spherical bodies interacting through Van der Waals forces at their closest approach distance.

Q4: What are typical values for the distance between surfaces?
A: For Van der Waals interactions, typical distances range from nanometers to micrometers, depending on the system.

Q5: Are there limitations to this calculation?
A: This calculation assumes ideal spherical bodies and only considers Van der Waals interactions, neglecting other potential forces.