Conservation of Energy: During any interaction, the total energy must remain constant; the energy gained or lost by an electron must exactly equal the energy of the photon involved.
The Planck-Einstein Relation: The energy of a photon () is defined by the equation , where is Planck's constant and is the frequency of the radiation.
Transition Condition: For an electron to move between two levels, and , the photon energy must satisfy .
Wavelength Relationship: Since , the energy can also be expressed in terms of wavelength as , showing that shorter wavelengths correspond to higher energy transitions.
Step 1: Identify Energy Levels: Determine the numerical energy values of the starting and ending states, usually provided in electron-volts (eV) or Joules (J).
Step 2: Calculate the Difference: Subtract the lower energy value from the higher energy value to find the energy gap, .
Step 3: Determine Photon Properties: Use to find the frequency or to find the wavelength of the emitted or absorbed light.
Step 4: Unit Conversion: Ensure all values are in SI units (Joules, meters, seconds) before calculation, or use the conversion .
Inverse Relationships: Always remember that the largest energy jump produces the shortest wavelength and the highest frequency.
The 'Exactly Match' Rule: In simple atomic absorption, a photon will pass through an atom without interaction if its energy does not exactly match a gap between allowed levels.
Visible Spectrum Context: Familiarize yourself with the energy range of visible light (approx. 1.8 eV to 3.1 eV) to quickly sanity-check if a calculated transition should be visible.
Check Your Units: Examiners often provide energy in eV but Planck's constant in ; failing to convert is the most common source of calculation errors.
The 'Halfway' Error: Students often mistakenly believe an electron can absorb half the energy of a large gap to move 'partway' between levels; in reality, the transition is all-or-nothing.
Frequency vs. Wavelength: Confusing the two leads to inverted results; remember that frequency is 'how fast it wiggles' (energy) and wavelength is 'the physical distance between peaks'.
Negative Energy Values: In many potential energy diagrams, energy levels are negative (representing bound states); when calculating , use absolute differences to avoid sign errors.