1. Analyzing the Hydrogen Balmer H-alpha Line
Physics StudentBackground
A student analyzing hydrogen emission spectroscopy needs to verify the transition parameters for the visible red emission line.
Problem
Calculate the transition energy and emitted photon wavelength for an electron dropping from n = 3 to m = 2.
How to use
Set the principal quantum number n to 3 and enter 2 in the transitionTo input.
Outcome
Calculates E₃ = −1.512 eV, r₃ = 0.476 nm, transition energy ΔE = 1.890 eV, and emitted wavelength λ = 656.112 nm (Balmer Hα line).
2. Evaluating Ground-State Hydrogen Properties
Science EducatorBackground
An instructor needs reference values for the ground-state hydrogen atom to create lecture slides on Bohr radius and ionization energy.
Problem
Find the baseline orbital radius, orbital velocity, period, and binding energy at n = 1.
How to use
Set the principal quantum number n to 1 and leave the transition field blank.
Outcome
Returns Bohr radius r₁ = 0.052918 nm (0.529 Å), ground-state energy E₁ = −13.606 eV, velocity v₁ = 2.188 × 10⁶ m/s (0.73% of c), and period T = 1.520 × 10⁻¹⁶ s.