Diamagnetic moment atom calculator

Use this Diamagnetic calculator to calculate Diamagnetic Moment of an Atom using electronic charge,electronic mass,atomic number,mean squared orbital radius and magnetic flux density.

Diamagnetic Moment of an Atom Calculator
Electronic Charge
Electron Mass
Atomic Number
Mean Squared Orbital Radius
Magnetic Flux Density
Diamagnetic Moment of an Atom: {{diamagneticMomentResult()}}

How to use Diamagnetic Moment of an atom Calculator?

Step 1 - Enter the Electronic Charge

Step 2 - Enter the Electron Mass

Step 3 - Calculate the Atomic Number

Step 4 - Enter the Mean Squared Orbital Radius

Step 5 - Enter the Magnetic Flux Density

Step 6 - Calculate the Diamagnetic Moment of an Atom

Diamagnetic Moment of an atom Formula:

m = $e^2$ / (6*me) * (z*$r^2$) * B

Where,

m = Diamagnetic Moment of an Atom

e = Electronic Charge

me = Electron Mass

z = Atomic Number

r = Mean Squared Orbital Radius

B= Magnetic Flux Density

Frequently Asked Questions

What is the diamagnetic moment and how is it different from paramagnetic moment?

The diamagnetic moment is an induced magnetic moment that opposes an external magnetic field. All atoms possess diamagnetism because electron orbits create opposing magnetic moments when exposed to external fields. Diamagnetic materials are weakly repelled by magnets. In contrast, paramagnetic atoms have unpaired electrons that align with external fields, causing attraction. Most materials show both effects, but diamagnetism is often dominated by paramagnetism in materials with unpaired electrons.

Why is the diamagnetic moment proportional to the atomic number and orbital radius?

The magnetic moment depends on the total negative charge contribution (proportional to atomic number Z) and how far electrons orbit from the nucleus (proportional to mean squared radius r²). More electrons further from the nucleus create stronger opposing magnetic moments when the field is applied. This relationship derives from Lenz’s law and quantum mechanical orbital theory.

How does magnetic field strength affect diamagnetic moment measurement?

The diamagnetic moment is an intrinsic property that becomes apparent when measured in the presence of an external magnetic field. The field strength determines the induced moment’s magnitude through the electron’s response. Stronger external fields induce proportionally larger diamagnetic moments, making measurement sensitivity dependent on field strength.

What are the quantum mechanical assumptions behind this calculation?

The formula assumes classical orbital motion of electrons, mean-field approximation for electron-nucleus interactions, and that the magnetic field is weak enough not to significantly perturb orbital structure. Full quantum treatment requires solving the Schrödinger equation, but this semi-classical approach provides excellent agreement for most atoms.

Diamagnetism and Debye screening both involve electron response to external perturbations. Debye screening describes how electrons rearrange to cancel external electric fields in plasmas, while diamagnetism describes orbital moment changes in magnetic fields. Both are fundamental electron-field interactions in condensed matter and plasma physics.

Physical Basis & References

This calculator applies Lenz’s Law and orbital diamagnetism theory:

$$m = -\frac{e^2}{6m_e}Z\langle r^2 \rangle B$$

Key Physics Principles:

  • Lenz’s Law - Induced magnetic moment opposes applied external field
  • Orbital Angular Momentum - Electron motion around nucleus creates magnetic moment
  • Quantum Mechanical Orbits - Mean squared radius describes electron probability distribution
  • Diamagnetic Response - All materials show this response; often masked by paramagnetism

Key Assumptions:

  • Classical orbital model of electrons (semi-classical approximation)
  • Weak external magnetic field (linear response regime)
  • Mean-field approximation for electron-nucleus and electron-electron interactions
  • Closed-shell or filled-shell electron configurations

Typical Range of Values:

  • Atomic number Z: 1 to 92 (hydrogen to uranium)
  • Mean squared orbital radius: 0.1 to 10 Ångströms (10⁻¹¹ to 10⁻¹⁰ m)
  • Magnetic flux density: 0.1 to 10 Tesla
  • Diamagnetic moment: 10⁻²⁸ to 10⁻²³ J/T (per atom)

Further Reading:

  • Kittel, C. (2005). Introduction to Solid State Physics, 8th Edition. Wiley.
  • Ashcroft, N.W. & Mermin, N.D. (1976). Solid State Physics. Holt, Rinehart and Winston.
  • Magnetic properties of elements - CRC Materials Science and Engineering Handbook

Conclusion

Read more about other Physics Calculator on below links