What is the relationship between frequency wavelength and photon energy of the electromagnetic wave

Answer

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Hint: The relationship between energy and wavelength or frequency can be well understood if you think in terms of a photon. We know that a photon is a discrete unit of quantized energy. Think about where the photon gets its energy from by employing Planck’s quantum theory. Given that photons are emitted in the range of the electromagnetic spectrum, i.e., radiation with increasing frequency and decreasing wavelength or vice versa, determine the correlation between the two and energy.

Formula Used:

$c=\nu\lambda$$E=h\nu$$E=\dfrac{hc}{\lambda}$

Complete Solution:

Let us begin by looking at the question in the context of photons. Photons are elementary particles that are essentially quantized electromagnetic radiation. This quantization implies that they hold packets of energy. The energy that they carry depends upon the kind of electromagnetic radiation that they quantized. This quantization of energy is consistent with Planck’s quantum theory which states that Energy is absorbed or radiated by atoms in discrete packets of energy called quanta, which are now known to be photons. Each quantum, or photon consists of a specific amount of energy that it can absorb or emit, which is directly proportional to the frequency of radiation. We know that the electromagnetic spectrum consists of electromagnetic radiation of varying frequencies and wavelengths. Therefore, according to Planck’s quantum theory we have:$E \propto \nu \Rightarrow E = h\nu$, where E is the photon energy, h ($6.626 \times 10^{-34}\;J.s$) is the proportionality (Planck’s) constant and $\nu$ is the frequency of radiation.Now, all electromagnetic radiation travels in the form of photons at the speed of light $c \approx 3 \times 10^8\;ms^{-1}$. If $\lambda$ is the wavelength of any radiation, then,$c=\nu \times \lambda \Rightarrow \nu = \dfrac{c}{\lambda}$Plugging this back into our energy expression in place of $\nu$, we get:$E = h\dfrac{c}{\lambda}$In essence, energy is directly proportional to the frequency of radiation but is inversely proportional to the wavelength. This means that energy increases with an increase in frequency or decrease in wavelength, and energy decreases with a decrease in frequency or an increase in wavelength.

Note:

Remember that Planck’s quantum theory, contrary to Maxwell's electromagnetic wave theory, suggests that radiant energy is not absorbed or emitted continuously but discontinuously in the form of small packets of energy called photons. Planck’s quantum theory was able to explain phenomena like the blackbody spectrum and photoelectric effect where Maxwell’s electromagnetic wave theory failed to do so since Maxwell’s theory entailed a continuous energy emission/absorption distribution.

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Answer:

From this equation, it is clear that the energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength. Thus as frequency increases (with a corresponding decrease in wavelength), the photon energy increases and visa versa.

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The electromagnetic spectrum

Wavelength and amplitude

Light is electromagnetic radiation which is visible to the human eye. Electromagnetic radiation is generated by the oscillation or acceleration of electrons or other electrically charged particles. The energy produced by this vibration travels in the form of electromagnetic waves. These waves are characterised by their wavelength (λ) which is the distance between successive peaks and is measured in units of length, and by their intensity, or amplitude, which is the height of each of those peaks.

To explain how light travels, it is considered a wave. However, light can also be considered particles when describing how it interacts with matter.

These particles called photons carry each a specific amount of energy. Light intensity increases with the number of photons. For example, intense red light used on a theatre stage and a traffic red light may consist of photons of the same energy but the first one is more intense due to the larger number of photons emitted.

Electromagnetic radiation extends from gamma rays (γ) through to long radio waves. This is often referred to as ‘the electromagnetic spectrum’. The energy of a wave depends on its wavelength: the longer the wavelength, the lower the energy. Therefore, in the electromagnetic spectrum, gamma rays have the highest energy, and long radio waves the lowest.

The sun emits visible light, but also infra-red (IR) and ultra-violet (UV) radiation.

The visible part of the electromagnetic spectrum only covers a small range of wavelengths, from 380 nm to 750 nm. In the electromagnetic spectrum, shorter wavelengths (from 10 nm to 380 nm) are ultraviolet (UV) and longer wavelengths (from 750 nm to 1 mm) are infrared (IR) radiation. Ultraviolet radiation carries more energy and infrared radiation less energy than visible light.

According to the wavelengths, the ultraviolet portion of the spectrum is further divided into: UVA (315 – 400 nm), UVB (280 – 315 nm) and UVC (100 – 280 nm). All radiation from the sun with a wavelength below 290 nm, that is most high-energy UV-radiation, is filtered out by the atmosphere before reaching the Earth’s surface. More...

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Interaction with skin and eyes depends on the wavelength of the radiation

Source: GreenFacts

Light is essential to life on Earth and affects humans and other living organisms in various ways. The interaction of light with our skin and eyes influences our perception of warmth and cold. The changes in the level and colour of light throughout the day and across different seasons help the body regulate periods of rest and activity.

The way electromagnetic radiation interacts with matter depends on its wavelength and therefore its energy. Radiation of short wavelength (below 200 nm, such as UVCs) has high energy and can set off damaging chemical processes in living cells. If DNA is damaged in this way, it can lead to mutations and potentially induce cancer. Radiation of longer wavelength is usually harmless, although it can warm up the tissue exposed.

When radiation reaches the skin or the eyes, it can be reflected or it can penetrate the tissue and be absorbed or scattered in various directions. The fate of this radiation in the body depends on its wavelength:

Visible light is usually scattered and is only strongly absorbed by some components such as pigments and blood. Pigments in specialized cells in the eye absorb visible radiation, triggering an electrical signal that travels through the optical nerve to the brain and allows us to see in colour.
Infrared radiation is not scattered but strongly absorbed by water – the main constituent of soft tissues – and this causes a heat sensation when the skin is exposed to sunlight.
Most ultraviolet radiation does not penetrate further than the upper layers of the skin (epidermis) as the human tissue absorbs the radiation very strongly. Although ultraviolet radiation has some beneficial effects such as helping production of vitamin D, in general it is considered to be harmful. This is because the absorbed energy not only produces heat but can also drive chemical reactions in the body. Most of these reactions are harmful and cause direct or indirect damage to proteins and DNA in the skin and eyes. Our skin is well adapted to the harmful effects of ultraviolet radiation and the damaged molecules and cells are usually repaired or replaced. Some people are particularly susceptible to ultraviolet and become sunburned even after extremely low exposures. Others show abnormal allergy-like skin reactions.

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