Consider the following statements about electromagnetic radiation and decide whether they are true or false. If they are false, correct them. (a) Photons of ultraviolet radiation have less energy than photons of infrared radiation. (b) The kinetic energy of an electron ejected from a metal surface when the metal is irradiated with ultraviolet radiation is independent of the frequency of the radiation. (c) The energy of a photon is inversely proportional to the wavelength of the radiation.

Electromagnetic radiation encompasses a wide range of wavelengths and frequencies, including radio waves, microwaves, infrared (IR), visible light, ultraviolet (UV), X-rays, and gamma rays. This radiation carries energy through space as both electric and magnetic waves. One significant characteristic of electromagnetic radiation is that it behaves both as a wave and as a particle (photon).

The energy of these photons varies inversely with their wavelength: the shorter the wavelength, the higher the energy. Hence, UV light has a higher frequency and energy than IR light, contrary to the false belief that UV photons have less energy than IR photons. The energy contained in electromagnetic waves plays a critical role in phenomena such as the photoelectric effect, where electrons are ejected from a material as a result of exposure to light.

The concept of photon energy is essential in understanding how light interacts with matter. Each photon has an energy associated with it that is proportional to its frequency, as represented by the equation \(E = hu\), where \(E\) stands for the energy of the photon, \(h\) is Planck's constant, and \(u\) denotes the frequency of the electromagnetic radiation. This relationship explains why UV photons have greater energy than IR photons, as they possess a higher frequency.

Contrary to the misconception, photon energy does increase with frequency, meaning photons with higher frequencies such as those from UV light can impart more energy upon interaction with matter, a fact critical in the photoelectric effect and many other physical processes.

Planck's constant (\(h\)) is a fundamental physical constant that is a crucial component in the formula for photon energy. It serves as a bridge between the energy and frequency of a photon, with the value of approximately \(6.626 \times 10^{-34} J \times s\). This constant, albeit incredibly small, has profound implications in quantum mechanics and describes the quantization of energy in the photoelectric effect.

This constant is pivotal in determining how much energy is contained in a single quantum (or photon) of electromagnetic radiation. The importance of Planck's constant becomes especially evident in the precise calculations needed to understand the behavior of photons and electrons at the microscopic scale.

The work function of a material is the amount of energy necessary to remove an electron from the surface of a solid. Different materials have different work functions, which play a key role in the photoelectric effect. If the photon energy is greater than the work function of the material, an electron is ejected.

It's a threshold energy for each material. The equation for the kinetic energy \(K.E. = hu - \phi\) illustrates that the work function (\(\phi\)) is the energy required for an electron to overcome the attractive forces in a material. This understanding corrects the false statement that the kinetic energy of ejected electrons is independent of radiation frequency, as it indeed relies on this interplay of incoming photon energy and the material's work function.

When a material is exposed to electromagnetic radiation of sufficient energy, electrons are ejected, possessing kinetic energy. The formula \(K.E. = hu - \phi\) shows that this kinetic energy is the difference between the incoming photon energy (\(hu\)) and the work function (\(\phi\)) of the material. A higher frequency of incident radiation implies higher photon energy, which, after overcoming the work function, results in greater kinetic energy of the ejected electron.

Therefore, it is incorrect to say that the kinetic energy is independent of the frequency of radiation, as the two are inextricably linked. Understanding the factors that influence the kinetic energy of electrons is essential for exploring various scientific and technological fields, including solar cells, photo sensors, and emission spectroscopy.