EEN2046 Physical Electronics Trimester 2 2012/13

Tutorial 1

The photoelectric effect1. A photoelectric experiment indicates that violet light of wavelength 420 nm is the longest

wavelength radiation that can cause photoemission of electrons from a particular multialkali photocathode surface.(a) What is the work function of the photocathode surface, in eV? [2.96eV](b) If a UV radiation of wavelength 300 nm is incident upon the photocathode surface, what will

be the maximum kinetic energy of the photoemitted electrons, in eV? [1.18eV](c) Given that the UV light of wavelength 300 nm has an intensity of 20 mW/cm2 , if the emitted

electrons are collected by applying a positive bias to the opposite electrode, what will be the photoelectric current density in mA/cm2? [4.84mAcm−2 ]

2. Consider the following metals and their work functions. For each metal, calculate the longest wavelength photon for photo-emmission. Which metal gives photoemission in the visible spectrum? [Cs, Rb and Sr]

Metal Al Be Cu Cs In Rb Sr Work function (eV) 4.25 3.92 4.40 1.81 3.80 2.16 2.35

Wave-particle duality, the Uncertainty Principle3. (i) The de Broglie wavelength of a particle λ = h/mv describes the wave-particle duality for

small particles such as electrons. What is the de Broglie wavelength of an electron at 100 eV? What is the wavelength for electrons at 12 keV, which is typical of electron microscopes? Comparing this to visible light, comment on the advantages of electron microscopes. [0.123 nm, 0.011 nm, better resolution]

4. (a) The position of an electron is determined to within 1Å. What is the minimum uncertainty in its momentum? [1.06×10−24 kgm/s](b) An electron’s energy is measured with an uncertainty of 1eV. What is the minimum uncertainty in the time over which the measurement was made? [6.59×10−16 s ].

Electron configuration, the periodic table5. The Determine whether each of the electron configurations given below is an inert gas, a halogen,

an alkali metal, an alkaline earth metal or a transition metal. Justify your choices.

(a) 1s2 2s2 2p6 3s2 2p6 3d7 4s2 [transition metal] (d) 1s2 2s2 2p6 3s2 [alkaline earth metal](b) 1s2 2s2 2p6 3s2 3p6 [inert gas] (e) 1s2 2s2 2p6 3s2 3p6 3d2 4s2 [transition metal](c) 1s2 2s2 2p5 [halogen] (f) 1s2 2s2 2p6 3s2 3p6 4s1 [alkali metal]

The wave function6. An electron in free space is described by a plane wave given by where

m−1 and rads−1.(a) Determine the phase velocity of the plane wave. [104 ms−1](b) Calculate the wavelength and momentum of the electron. [4.19 nm]

7. An electron is bound in a one-dimensional infinite potential well with a width of 10 nm. Determine the electron energy levels for the wave numbers n = 1, 2 and 3. [3.76×10−3, 1.50×10−2, 3.38×10−2 eV]

Deepak Kumar

EEN2046 Physical Electronics Trimester 2 2012/13

8. A semiconductor device requires a transmission coefficient T = 10−5 for an electron tunneling through a rectangular barrier with a height of V0 = 0.4 eV. If the electron energy is 0.04 eV, determine the maximum barrier width. [1.93 nm]

Deepak Kumar