What is the Planck constant (definitionally)?
The Planck constant is a physical constant, summarised thus: "A photon's energy is its frequency multiplied by the Planck constant"
This is summarised by the formula, E = hf.
The above is sometimes called the Planck-Einstein (or just the Planck) relation. This is considered part of quantum mechanics.
Planck calculated the value of h from experimental data on black-body radiation.
What this helps us understand phenomena such as the photoelectric effect and black-body radiation.
How is frequency of a photon measured?
For low-frequency photons, you can directly measure the oscillation frequency of the EM field using electronic frequency counters.
What are the relevant units? (Hint: go from the known, to the unknown)
E is energy, measured in Joules. Frequency has units hertz, which means "per second" or "cycles (scalar, dimensionless quantity) per second". The Planck constant, therefore, by implication, must have the units J-s (Joule-seconds).
OK. So the Planck constant is not just a scaling factor on frequency - to level it up to the energy level of the photon - it is something more meaningful. Planck introduced it as a "quantum of action" - the smallest possible unit of physical action. Its dimension of energy x time represents action.
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