11.7 The work function for a certain metal is 4.2 eV. Will this metal give hotoelectric emission for incident radiation of wavelength 330 nm?

11.6 EINSTEIN’S PHOTOELECTRIC EQUATION: ENERGY QUANTUM OF RADIATION In 1905, Albert Einstein (1879-1955) proposed a radically new picture of electromagnetic radiation to explain photoelectric effect. In this picture, photoelectric emission does not take place by continuous absorption of energy from radiation. Radiation energy is built up of discrete units – the so called quanta of energy of radiation. Each quantum of radiant energy has energy hn, where h is Planck’s constant and n the frequency of light. In photoelectric effect, an electron absorbs a quantum of energy (hn ) of radiation. If this quantum of energy absorbed exceeds the minimum energy needed for the electron to escape from the metal surface (work function f0), the electron is emitted with maximum kinetic energy Kmax = hn – f0 (11.2) More tightly bound electrons will emerge with kinetic energies less than the maximum value. Note that the intensity of light of a given frequency is determined by the number of photons incident per second. Increasing the intensity will increase the number of emitted electrons per second. However, the maximum kinetic energy of the emitted photoelectrons is determined by the energy of each photon. Equation (11.2) is known as Einstein’s photoelectric equation. We now see how this equation accounts in a simple and elegant manner all the observations on photoelectric effect given at the end of sub-section 281 11.4.3. Reprint 2025-26 Physics · According to Eq. (11.2), Kmax depends linearly on n, and is independent of intensity of radiation, in agreement with observation. This has happened because in Einstein’s picture, photoelectric effect arises from the absorption of a single quantum of radiation by a single electron. The intensity of radiation (that is proportional to the number of energy quanta per unit area per unit time) is irrelevant to this basic process. · Since Kmax must be non-negative, Eq. (11.2 ) implies that photoelectric emission is possible only if h n > f0 or n > n0 , where φ0 Albert Einstein (1879 – n0 = (11.3) 1955) Einstein, one of the h greatest physicists of all Equation (11.3) shows that the greater the work time, was born in Ulm, function f0, the higher the minimum or threshold Germany. In 1905, he frequency n0 needed to emit photoelectrons. Thus, published three path- breaking papers. In the there exists a threshold frequency n0 (= f0/h) for the first paper, he introduced metal surface, below which no photoelectric emission the notion of light quanta is possible, no matter how intense the incident (now called photons) and radiation may be or how long it falls on the surface. used it to explain the · In this picture, intensity of radiation as noted above, features of photoelectric effect. In the second paper, is proportional to the number of energy quanta per he developed a theory of unit area per unit time. The greater the number of Brownian motion, energy quanta available, the greater is the number of confirmed experimentally a electrons absorbing the energy quanta and greater, few years later and provided therefore, is the number of electrons coming out of a convincing evidence of the atomic picture of matter. the metal (for n > n0). This explains why, for n > n0, The third paper gave birth photoelectric current is proportional to intensity. to the special theory of · In Einstein’s picture, the basic elementary process relativity. In 1916, he involved in photoelectric effect is the absorption of a published the general light quantum by an electron. This process is1955) theory of relativity. Some of – Einstein’s most significant instantaneous. Thus, whatever may be the intensity later contributions are: the i.e., the number of quanta of radiation per unit area notion of stimulated per unit time, photoelectric emission is instantaneous. emission introduced in an Low intensity does not mean delay in emission, since(1879 alternative derivation of the basic elementary process is the same. Intensity Planck’s blackbody radiation law, static model only determines how many electrons are able to of the universe which participate in the elementary process (absorption of a started modern cosmology, light quantum by a single electron) and, therefore, the quantum statistics of a gas photoelectric current.EINSTEIN of massive bosons, and a Using Eq. (11.1), the photoelectric equation, Eq. (11.2), critical analysis of the foundations of quantum can be written as mechanics. In 1921, he was e V0 = h n – f0; for ν≥ ν0 awarded the Nobel Prize in physics for his contribution h φ0 (11.4) ν −ALBERT to theoretical physics and or V0 = the photoelectric effect. e e This is an important result. It predicts that the V0 282 versus n curve is a straight line with slope = (h/e), Reprint 2025-26 Dual Nature of Radiation and Matter independent of the nature of the material. During 1906-1916, Millikan performed a series of experiments on photoelectric effect, aimed at disproving Einstein’s photoelectric equation. He measured the slope of the straight line obtained for sodium, similar to that shown in Fig. 11.5. Using the known value of e, he determined the value of Planck’s constant h. This value was close to the value of Planck’s contant (= 6.626 × 10–34J s) determined in an entirely different context. In this way, in 1916, Millikan proved the validity of Einstein’s photoelectric equation, instead of disproving it. The successful explanation of photoelectric effect using the hypothesis of light quanta and the experimental determination of values of h and φ0, in agreement with values obtained from other experiments, led to the acceptance of Einstein’s picture of photoelectric effect. Millikan verified photoelectric equation with great precision, for a number of alkali metals over a wide range of radiation frequencies.

11.2 ELECTRON EMISSION We know that metals have free electrons (negatively charged particles) that are responsible for their conductivity. However, the free electrons cannot normally escape out of the metal surface. If an electron attempts to come out of the metal, the metal surface acquires a positive charge and pulls the electron back to the metal. The free electron is thus held inside the metal surface by the attractive forces of the ions. Consequently, the electron can come out of the metal surface only if it has got sufficient energy to overcome the attractive pull. A certain minimum amount of energy is required to be given to an electron to pull it out from the surface of the metal. This minimum energy required by an electron to escape from the metal surface is called the work function of the metal. It is generally denoted by f0 and measured in eV (electron volt). One electron volt is the energy gained by an electron when it has been accelerated by a potential difference of 1 volt, so that 1 eV = 1.602 ×10–19 J. This unit of energy is commonly used in atomic and nuclear physics. The work function (f0) depends on the properties of the metal and the nature of its surface. The minimum energy required for the electron emission from the metal surface can be supplied to the free electrons by any one of the following physical processes: (i) Thermionic emission: By suitably heating, sufficient thermal energy can be imparted to the free electrons to enable them to come out of the 275 metal. Reprint 2025-26 Physics (ii) Field emission: By applying a very strong electric field (of the order of 108 V m–1) to a metal, electrons can be pulled out of the metal, as in a spark plug. (iii) Photoelectric emission: When light of suitable frequency illuminates a metal surface, electrons are emitted from the metal surface. These photo(light)-generated electrons are called photoelectrons. 11.3 PHOTOELECTRIC EFFECT 11.3.1 Hertz’s observations The phenomenon of photoelectric emission was discovered in 1887 by Heinrich Hertz (1857-1894), during his electromagnetic wave experiments. In his experimental investigation on the production of electromagnetic waves by means of a spark discharge, Hertz observed that high voltage sparks across the detector loop were enhanced when the emitter plate was illuminated by ultraviolet light from an arc lamp. Light shining on the metal surface somehow facilitated the escape of free, charged particles which we now know as electrons. When light falls on a metal surface, some electrons near the surface absorb enough energy from the incident radiation to overcome the attraction of the positive ions in the material of the surface. After gaining sufficient energy from the incident light, the electrons escape from the surface of the metal into the surrounding space. 11.3.2 Hallwachs’ and Lenard’s observations Wilhelm Hallwachs and Philipp Lenard investigated the phenomenon of photoelectric emission in detail during 1886-1902. Lenard (1862-1947) observed that when ultraviolet radiations were allowed to fall on the emitter plate of an evacuated glass tube enclosing two electrodes (metal plates), current flows in the circuit (Fig. 11.1). As soon as the ultraviolet radiations were stopped, the current flow also stopped. These observations indicate that when ultraviolet radiations fall on the emitter plate C, electrons are ejected from it which are attracted towards the positive, collector plate A by the electric field. The electrons flow through the evacuated glass tube, resulting in the current flow. Thus, light falling on the surface of the emitter causes current in the external circuit. Hallwachs and Lenard studied how this photo current varied with collector plate potential, and with frequency and intensity of incident light. Hallwachs, in 1888, undertook the study further and connected a negatively charged zinc plate to an electroscope. He observed that the zinc plate lost its charge when it was illuminated by ultraviolet light. Further, the uncharged zinc plate became positively charged when it was irradiated by ultraviolet light. Positive charge on a positively charged zinc plate was found to be further enhanced when it was illuminated by ultraviolet light. From these observations he concluded that negatively charged particles were emitted from the zinc plate under the action of ultraviolet light. After the discovery of the electron in 1897, it became evident that the incident light causes electrons to be emitted from the emitter plate. Due276 Reprint 2025-26 Dual Nature of Radiation and Matter to negative charge, the emitted electrons are pushed towards the collector plate by the electric field. Hallwachs and Lenard also observed that when ultraviolet light fell on the emitter plate, no electrons were emitted at all when the frequency of the incident light was smaller than a certain minimum value, called the threshold frequency. This minimum frequency depends on the nature of the material of the emitter plate. It was found that certain metals like zinc, cadmium, magnesium, etc., responded only to ultraviolet light, having short wavelength, to cause electron emission from the surface. However, some alkali metals such as lithium, sodium, potassium, caesium and rubidium were sensitive even to visible light. All these photosensitive substances emit electrons when they are illuminated by light. After the discovery of electrons, these electrons were termed as photoelectrons. The phenomenon is called photoelectric effect.