Wavelength, frequency, energy [with exercise questions]

As we've discussed before, electromagnetic radiation is essentially electromagnetic wave (or a photon in a particulate view) and have no mass. The important properties that differs different electromagnetic radiations is their wavelength, which also determines frequency and energy.

Wavelength

Wavelength, distance between corresponding points of two consecutive waves. “Corresponding points” refers to two points or particles in the same phase. Wavelength is usually denoted by the Greek letter lambda (λ); it is equal to the speed (v) of a wave train in a medium divided by its frequency (f): λ = v/f.

Frequency

Frequency is the number of occurrences of a repeating event per unit of time. Frequency is measured in units of hertz which is equal to one occurrence of a repeating event per second. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. Frequency and period is usually denoted as f and T, respectively.

Wave-particle duality

According to wave-particle duality, every particle may be described as either a particle or a wave. Simpliy speaking, every particle can be observed as a wave especially in a high speed close to the velocity of light. The electromagnetic wave can also be treated as a particle, which is a photon. Wave-particle duality theory express the inability of the classical concepts “particle” or “wave” to fully describe the behaviour of quantum-scale object and connect the particulate properties and wave properties together.

Energy

In physics, and in particular as measured by radiometry, radiant eergy is the energy of electromagnetic and gravitational radiation. The quantity of radiany energy may be calculated by integrating radiant flux with respect to time. The symbol Q_e is often used throughout literature to denote radiant energy. The power of radiation desicribes the energy transmision of power from one location to another in a unit time.

However, the ability and strength of ionization depends on the energy of a single radiant particle (including photon).

For example, the energy of a photon is $$E = \frac{hc}{\lambda}$$ , where h is Planck constant.

The energy of a real particle is $$ E = \frac{h^{2}f^{2}}{2m}$$

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