Radius of Nth Orbit of Electron Calculator

Formula Used:

\[ r_n = \frac{[Coulomb] \times n^2 \times [hP]^2}{M \times [Charge-e]^2} \]

Radius of nth Orbit of Electron:

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1. What is the Radius of Nth Orbit of Electron?

The radius of the nth orbit of an electron is defined as the distance from the nucleus to the electron in a particular energy level or shell in an atom, according to Bohr's model of the atom.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_n = \frac{[Coulomb] \times n^2 \times [hP]^2}{M \times [Charge-e]^2} \]

Where:

\( [Coulomb] \) — Coulomb constant (8.9875×10⁹ N·m²/C²)
\( n \) — Quantum number (principal quantum number)
\( [hP] \) — Planck's constant (6.626070040×10⁻³⁴ J·s)
\( M \) — Mass of the particle (kg)
\( [Charge-e] \) — Charge of electron (1.60217662×10⁻¹⁹ C)

Explanation: This formula calculates the radius of the nth orbit of an electron in Bohr's atomic model, which describes electrons orbiting the nucleus in specific energy levels.

3. Importance of Orbit Radius Calculation

Details: Calculating the radius of electron orbits is fundamental to understanding atomic structure, energy levels, and the quantum mechanical behavior of electrons in atoms. It's essential for studying atomic spectra and chemical bonding.

4. Using the Calculator

Tips: Enter the quantum number (n) as a positive integer and the mass of the particle in kilograms. The quantum number must be at least 1, and the mass must be greater than 0.

5. Frequently Asked Questions (FAQ)

Q1: What is the quantum number (n)?
A: The quantum number (n) is the principal quantum number that specifies the energy level and size of the electron orbit. It can be any positive integer (1, 2, 3, ...).

Q2: Why does the orbit radius increase with n²?
A: The radius increases with the square of the quantum number because higher energy levels have electrons that are farther from the nucleus, with more space between energy levels.

Q3: What particles can this calculator be used for?
A: This calculator can be used for any charged particle, but it's primarily designed for electrons in atomic orbits. For other particles, you would need to input the appropriate mass.

Q4: Are there limitations to this formula?
A: Yes, this formula is based on Bohr's model, which is a simplified model of the atom. It doesn't account for quantum mechanical effects fully and is most accurate for hydrogen-like atoms.

Q5: How accurate is this calculation for real atoms?
A: For hydrogen and hydrogen-like ions, this calculation is quite accurate. For multi-electron atoms, the results are approximate due to electron-electron interactions not accounted for in Bohr's model.