Convert between energy units:

a. 231 cal to kJ b. 132 x 104 kJ to kcal

c. 4.99 x 103 kJ to kWh d. 2.88 x 104 J to Cal

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: a) According to Planck’s quantum theory of radiation, the amount of energy associated with a quantum(in case of light, the quantum of energy is often called photon) of radiation is proportional to the frequency of light, E = h ---(1), where h is a universal constant called Planck’s constant. is the frequency and E is the energy of a photon. Or, E = hc/ -------(2), where, is the wavelength of light and c is the velocity. Step2: Here, given minimum energy required = 6.94 x 10 -19J Planck's constant, h = 6.626 x 10 J.s -34 Substituting the values in equation (1), we get, 6.94 x 10 -19J = (6.626 x 10 J.s) x -19 -34 = (6.94 x 10 J) / (6.626 x 10 J.s) = 1.05 x 10 s . -1 Thus, minimum frequency required to eject an electron is 1.05 x 10 s . 15 -1 Step3: b) From equation (2), = hc/E Here, Velocity of light, c = 3 x 10 m/sec 8 Energy, E = 6.94 x 10 -19J Substituting the values, we get, = [(6.626 x 10 J.s) x (3 x 10 m/sec)] / (6.94 x 10 -19J) -7 = 2.86 x 10 m. Thus, wavelength of the light = 2.86 x 10 m. -7 Step4: c) For each metal a minimum frequency of light called threshold frequency is required below which there is no ejection of electrons from the surface of the metal. The minimum frequency of light necessary to emit electrons from titanium via the photoelectric effect is 1.05 x 10 s and the frequency of visible light ranges from (4 x 10 s ) to (8 x 10 s ) which is less14 -1 than the threshold frequency of titanium. Therefore, it is not possible to eject electrons from titanium metal using visible light. Step5: d) Wavelength of the irradiated light = 233 nm = 233 x 10 m -9 [1 nm = 10 m]-9 = 2.33 x 10 m -7 -34 Planck's constant, h = 6.626 x 10 J.s Velocity of light, c = 3 x 10 m/sec 8 Substituting the values in equation (2), we get, -34 8 -7 E = [(6.626 x 10 J.s) x (3 x 10 m/sec)] / (2.33 x 10 m) = 8.53 x 10 J -19 -19 Thus, energy of the irradiated radiation = 8.53 x 10 J Step6: Therefore, kinetic energy of the emitted electron = Energy of the radiation - minimum energy needed to eject an electron = (8.53 x 10 J) - (6.94 x 10 -19J) -19 = 1.59 x 10 J. Step7: -6 -6 e) Total energy of the light = 2.00 J = 2 x 10 J [1 J = 10 J] Energy required to eject an electron = 6.94 x 10 -19J Therefore, total number of electrons ejected = Total energy of light / energy required to eject 1 electron = (2 x 10 J) / (6.94 x 10 -19J) 13 = 0.288 x 10 12 = 2.88 x 10 . Thus, 2.88 x 10 electrons were ejected. --------------------------------------