1. What is Quantum Number (n)?

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

2. How Does the Calculator Work?

The calculator uses the simple relationship:

Where:

• \( n \) — Principal quantum number
• Energy Level — Positive integer (1, 2, 3, ...)

Explanation: The principal quantum number directly corresponds to the energy level of an electron in an atom.

3. Importance of Quantum Number

Details: The principal quantum number is fundamental in quantum mechanics as it determines the electron's energy and the size of its orbital. Higher values of n correspond to higher energy levels and larger orbitals.

4. Using the Calculator

Tips: Simply enter the energy level as a positive integer (1 or greater). The calculator will return the corresponding principal quantum number.

5. Frequently Asked Questions (FAQ)

Q1: What values can n take?
A: n can be any positive integer (1, 2, 3, ...). There is no theoretical upper limit, though practical limits exist for known elements.

Q2: How does n relate to electron energy?
A: Higher n values correspond to higher energy levels. The energy is inversely proportional to n² in hydrogen-like atoms.

Q3: What is the ground state quantum number?
A: The ground state corresponds to n=1, which is the lowest energy state of an electron in an atom.

Q4: Can n be zero or negative?
A: No, n must be a positive integer starting from 1. Zero or negative values are not physically meaningful.

Q5: How does n relate to orbital size?
A: The average distance of the electron from the nucleus increases with n², meaning higher n orbitals are significantly larger.