Bohr Model of the Hydrogen Atom

Step 1: Write the relevant Bohr postulate. Step 2: Identify n, initial level, and final level. Step 3: Apply L = nh/2π for orbit questions or hν = energy difference for transition questions. Step 4: Keep units consistent. Step 5: Interpret whether the transition is emission or absorption.

Draw a central nucleus with circular allowed orbits labelled n = 1, n = 2, n = 3. Show an inward arrow for emission and an outward arrow for absorption. Label photon hν for the transition.

A common wrong answer is taking the numerical energy difference as negative for emitted photon energy. Photon energy must be reported as a positive amount; the atom's energy decreases during emission.

Bohr's model of hydrogen states that the electron can revolve only in certain stable stationary orbits without radiating energy, and radiation is emitted or absorbed only when the electron jumps between allowed energy levels.

Bohr's model of hydrogen states that the electron can revolve only in certain stable stationary orbits without radiating energy, and radiation is emitted or absorbed only when the electron jumps between allowed energy levels. Angular momentum quantisation: L = mvr = nh/2π, where m is electron mass in kg, v is orbital speed in m s^-1, r is orbit radius in m, n is the principal quantum number, and h is Planck's constant in J s. Transition rule: hν = Ei - Ef for emission, where ν is frequency in Hz and energies are in joule or consistently in eV. Use for hydrogen or hydrogen-like one-electron systems. For hydrogen, the first orbit has n = 1 and the second orbit has n = 2. A transition from n = 3 to n = 2 gives a photon in the Balmer series because the final level is n = 2.

Bohr modified the Rutherford model by adding quantum conditions. The electron is allowed only in orbits where its angular momentum is an integral multiple of h divided by 2π. While in such an orbit, it does not radiate energy. When it moves from a higher energy level to a lower energy level, it emits a photon; when it absorbs the right energy, it moves to a higher level. The model works best for hydrogen and hydrogen-like single-electron species. Angular momentum quantisation: L = mvr = nh/2π, where m is electron mass in kg, v is orbital speed in m s^-1, r is orbit radius in m, n is the principal quantum number, and h is Planck's constant in J s. Transition rule: hν = Ei - Ef for emission, where ν is frequency in Hz and energies are in joule or consistently in eV. Use for hydrogen or hydrogen-like one-electron systems. An electron in hydrogen jumps from n = 3 to n = 2. Using En = -13.6/n^2 eV, E3 = -13.6/9 = -1.51 eV and E2 = -13.6/4 = -3.40 eV. Photon energy for emission = E3 - E2 = (-1.51) - (-3.40) = 1.89 eV. Interpretation: the atom emits a photon of energy 1.89 eV in the Balmer series. Questions may ask for Bohr's postulates, the meaning of stationary orbit, angular momentum quantisation, photon energy in a transition, or why Bohr's model improves Rutherford's model. A common wrong answer is taking the numerical energy difference as negative for emitted photon energy. Photon energy must be reported as a positive amount; the atom's energy decreases during emission.