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MT1_Solutions - ECE344 Midterm Exam 1 Solutions 1 Problem...

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ECE344, Midterm Exam 1: Solutions October 19, 2009 1. Problem: The workfunction of a material is defined as the energy required to remove an electron from the material and is usually indicated by the Greek letter χ (pron: ‘khi’). The workfunction of gold is χ Au = 4 . 9 eV, the workfunction of cesium is χ Cs = 1 . 9 eV. a. Calculate the maximum wavelength (in nm) of light required to remove an electron from Au via the photoelectric e ff ect. b. Do the same for Cs. Solution: Since λ = c ν = 2 π ¯ hc h ν = 2 π ¯ h E , (1) or, expressing the energy in eV: λ = 2 π ¯ h eE , (2) using E = χ Au we have λ = 253 nm and using E = χ Cs we get λ = 653 nm. 2. Problem: Electrons in a ‘swarm’ at thermal equilibrium have each an average kinetic energy of (3 / 2) k B T . a. Calculate the value of (3 / 2) k B T in eV. b. Calculate the velocity (in cm/s) of an electron having a kinetic energy equal to the average energy (3 / 2) k B T . This is the so-called ‘thermal velocity’. c. Calculate its average de Broglie wavevelength in cm. This is called the ‘thermal wavelength’.
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