1. What is the Principal Quantum Number?

The principal quantum number (n) describes the energy level and size of an electron orbital in an atom. It is a positive integer (1, 2, 3, ...) that determines the electron's energy and most probable distance from the nucleus.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( n \) — Principal quantum number (dimensionless integer)
• \( Z \) — Atomic number (number of protons)
• \( E \) — Energy of the electron (eV, must be negative)
• 13.6 — Rydberg constant for hydrogen (eV)

Explanation: The equation relates the energy of an electron in a hydrogen-like atom to its principal quantum number.

3. Importance of Principal Quantum Number

Details: The principal quantum number is fundamental in quantum mechanics as it determines the electron's energy level, orbital size, and helps explain atomic spectra and chemical properties.

4. Using the Calculator

Tips: Enter atomic number (Z) as a positive integer and energy (E) as a negative value in electron volts (eV). The calculator will return the principal quantum number.

5. Frequently Asked Questions (FAQ)

Q1: What values can n take?
A: n can be any positive integer (1, 2, 3, ...). n=1 represents the ground state.

Q2: Why must the energy be negative?
A: Negative energy indicates a bound electron in the atom. Positive energy would mean the electron is unbound.

Q3: Is this only for hydrogen?
A: The formula works best for hydrogen-like atoms (single electron systems), but can approximate values for other atoms.

Q4: What's the physical meaning of n?
A: Higher n values correspond to electrons in larger orbitals with higher energy that are less tightly bound to the nucleus.

Q5: How is this related to atomic spectra?
A: Transitions between different n levels produce the characteristic spectral lines of elements.