Question

The fermi energy of silver is given as 5.49 eV. a) Find the densities of electron and atom per volume. b) Find the fermi velocity of electron in silver c) The current value flowing through silver is 2 A. The cross sectional area of silver is 0.5 cm2 . Find the drift velocity of electron in silver according to given conditions. d)Find the collision time  for an electron for sliver. (the definition of current density is the current per cross sectional area, the resistivity value of silver is 1.59x10-8 ohm.m,)

Answer 1

0.5x10'y 5.86 110 x 1.64 10 (a) The ferme energy Ps 23 (373) given forme energy of silver Ef = 5.4g eV given by Er t² 2 n = number density of elections he of electron (32?n) where = mass Er am 2 3/ 2m Er 32 (m 2 me? Er 3 h² tre? 2x0.5 MeV x 5.49 ev (197 Mev - fom ) using 37²n t2 tc 197 Mev-fm mee? 0,5 MeV = 0.581or ev h =) shi 6 3/2 34² -15 i1fm = 10 28 elections /m² 1x5.49x10 (1977² fm² n = 5.86 X10 number density is (b) using Ep = 1 m. Ne The fermi velocity Ve 28 h = 5.868 10 elections/m3 so The 2 2&f 286 so he (= 3 XO 8 m/sec up = 3x108 / 2X5.49 ev 10.5rlorer 6 The fermi 1.39 Xlo m/sec velocity ve (C) The using cross Gel final area of siluer A = 0.5 cm = 0.5X10M2 current through silued i = 2 A cament density J = nehva where I = 1 A so drift velocity Ved = Ane Isneva A 2. = 0.4266 8 10 m/rec va 28 19

0 of -6 m/sec The drift velocity is Vd = 4.266 XIO -8 (1) giver resistivity is 1.59 X10 is using conductivity given by is R-m P ne?e m 8 z = mo he2 m -31 9.1 x 10 5.86 X10281.59 x16 Ⓡx (116 XIÓ The collision time Ps T = h) е? ( -31 9.1 X10 z = -3 | 0.3815 810 28 2 5.868 10 X1.59 X 10 °x(1.6 X10 o'') 38 20 =0.3815 810 -18 10 10 x 10 -14 7= 3.815 8 10 sec -14 3.815 XIO sec The collision time is て