In this chapter, we have learned about the photoelectric effect and its impact on the formulation of light as photons. We have also seen that some anomalous electron configurations of the elements are particularly favorable if each atom has one or more half-filled shell, such as the case for the Cr atom with its [Ar]4s13d5 electron configuration. Let’s suppose it is hypothesized that it requires more energy to remove an electron from a metal that has atoms with one or more half-filled shells than from those that do not. (a) Design a series of experiments involving the photoelectric effect that would test the hypothesis, (b) What experimental apparatus would be needed to test the hypothesis? It’s not necessary that you name actual equipment but rather that you imagine how the apparatus would work—think in terms of the types of measurements that would be needed, and what capability you would need in your apparatus, (c) Describe the type of data you would collect and how you would analyze the data to see whether the hypothesis were correct, (d) Could your experiments be extended to test the hypothesis for other parts of the periodic table, such as the lanthanide or actinide elements?
Solution: The phenomenon of ejection of electrons from the surface of a metal when light of suitable frequency strikes on it, is called photoelectric effect. Step1: Half filled orbitals(containing one electron per orbital) have lower energy and are therefore extra stable. This extra stability is mainly due to their symmetrical arrangement and large exchange energy. Due to this stability, more energy is required to remove an electron from half filled shell. Step2: a) The apparatus showing photoelectric effect consists of a cell having an evacuated chamber which contains two electrodes connected to an external circuit. The metal that exhibits the photoelectric effect is mabe negative electrode. When light of sufficiently high energy strikes the metal, the electrons are ejected from its surface and move towards the positive electrode and form the current flowing through the circuit. b) The diagrammatic representation of the apparatus is given below: Photoelectric experiment with high energy blue light Photoelectric experiment with low energy red light Step3: c) Experimental studies of photoelectric effect led to the following observations: For each metal a minimum frequency of light is required below which there is no ejection of electrons from the surface of the metal. This minimum frequency is known as the threshold frequency, , foothe metal. The kinetic energy of emitted electrons increases linearly with the increase in the frequency of light used. Kinetic energy does not depend on the intensity of light. The ejection of electrons from the surface of the metal is instantaneous if light with frequency higher than the threshold frequency of the metal is used. The number of ejected electrons from the metal surface is proportional to the intensity of irradiated light. Step4: The number of electrons ejected and the kinetic energy associated with them should depend on the brightness of light. However, as has been discussed above though the number of electrons ejected depends upon brightness of light, the kinetic energy of the lectrons does not. For example, red light( = 4.3 - 4.6 x 10 s ) of any brightness may shine on a potassium surface for 14-1 hours but it does not eject electrons. But yellow light ( = 5.1 - 5.2 x 10 s ) of even a very weak brightness ejects electrons. This is because the threshold frequency ( ) for potassium 14 -1 o metal is 5.0 x 10 s and light of frequency more than (i.e., yello light and not red light) can cause photoelectric effect. Step5: d) Lanthanides and Actinides are f-block elements(last electron enters the f-orbital). Only the three lanthanide elements Cerium, Lutetium and Gadolinium have a d electron and hence behaves as a d-block element. Since, the photoelectric effect is not extended to f-block elements, therefore, it can be used to test the hypothesis of only the three lanthanides and not the actinides. --------------------------------