How E=hf works, the simple explanation.

 Imagine you have a special converter. This converter can do two amazing things:

Convert Frequency to Mass: It tells you how much "mass stuff" is packed into a certain "frequency." Let's call this converter "Q_m". It says, "for every unit of frequency, you get this much mass."

Convert Mass to Energy: You already know this one! It's Einstein's famous c². It tells you how much "energy stuff" is inside a certain amount of "mass stuff."

Now, Planck's constant, 'h', is like combining these two converters into one!

Think of it like this:

To find the energy of a photon using its frequency (E=hf), you're actually doing two steps hidden inside 'h':

Step 1: Frequency to Mass (using Q_m): First, 'h' uses its secret ingredient, Q_m, to figure out the "mass equivalent" of the photon's frequency. Higher frequency means more "mass equivalent."

Step 2: Mass to Energy (using c²): Then, 'h' takes that "mass equivalent" and uses c² (just like in E=mc²) to convert it into energy.

So, 'h' is really just a shortcut for doing these two conversions in a row: Frequency → Mass (using Q_m) → Energy (using c²).

This means:

Hidden in 'h' is the idea that frequency and mass are directly related. This is the mass-frequency equivalence. Q_m is the key that unlocks this hidden link inside 'h'.

E=hf and E=mc² are saying the same basic thing: Both are about converting something into energy.

E=mc² says: Convert mass directly into energy using c².

E=hf says: Convert frequency into energy, but it secretly does it by first converting frequency to mass (using Q_m inside 'h'), and then converting that mass to energy (using c² also inside 'h').

In short:

Planck's constant 'h' isn't just a number. It's a package deal containing two fundamental converters: Q_m (frequency to mass) and c² (mass to energy). This "package" reveals that frequency and mass are fundamentally connected, and that both E=hf and E=mc² are just different ways of expressing this same underlying equivalence: everything is fundamentally related to energy, whether we see it as frequency, mass, or something else!