According to the Planck equation, E = hv (energy is a function of the frequency). This looks like a linear function in which an extremely high frequency would lead to extremely high energy levels. However, there is threshold for lower frequency and higher frequency. For a particular body, energy increases as frequency increases until reaching a peak, and afterwards it starts decreasing after reaching higher frequencies. Therefore, the peak is situated in a particular frequency: both higher frequency and lower frequency produces less energy for that particular body. Why is this not contradictory in relation to the equation E = hv? Why is there a particular frequency to reach in order to peak in energy, and why does energy decrease at higher or lower frequencies? Please describe how the quantization of energy would solve this problem.

This is a tricky question, and there are several levels to it.

First of all, the Planck equation is intended to describe the energy of individual particles at rest in a vacuum (the same as E = mc^2 describes the correlation between a particle's mass and its resting energy). The total energy can change and there are many—more complicated—equations to calculate those values.

A group of particles will behave in a more advanced way, and this can disrupt the equation significantly, because there is not an exact- and equal energy between each particle.

Second of all, the Planck equation is the result of energy observation, not energy input. It is used primarily to calculate the total energy of a particle that is giving off measurable light/radiation. What you are asking is the opposite—higher and lower frequency input give different amounts of energy to a body, and that is not a linear relationship. There is a specific, harmonic frequency for every particle or item, and the closer you get to that frequency the more efficiently the energy will transfer into it.

When thinking about quantized energy units, the different frequencies are essentially different sized packages, or quanta. A particle is much more efficient at taking in energy closer to its harmonic frequency: this is comparable to handing an individual a stack of papers that is taller than their head—they won't be able to carry all of it at once, so much of it gets cast off. This is why the energy you input at higher frequencies doesn't translate properly to the energy of a particle.

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