Question

Problem 40.24 - Enhanced - with Feedback An electron approaches a 1.6-nm-wide potential energy barrier of height 6.8 eV You may want to review (Pages 1169 - 1172) Part A What energy electron has a tunneling probability of 10%? Express your answer to three significant figures and include the appropriate units. Value Units Submit Request Answer - Part B What energy electron has a tunneling probability of 1.0%? Express your answer to three significant figures and include the appropriate units. E Value Units Submit Request Answer

Answer 1

solution Given Election approaches 1.6 mm height 6.8 ev Palth To find eneegy election has a - tonneling probability of 10% We know n= h . 27152m ( U-E) n = 6.63481034 7.822x10 % 2TS2x 9.1141631(0-€) Jose LO w=1.6mm = 1.6*10 m Vo = 6.8ev - 6.8 x1,6x1019 1.083 xjól! I Probability P = -20 1:26 - 2x1,6x109 23.2 x19 " in (P) en (P) from 0 "2=(7.822 X162012 Us-E UE =(7-122 x17 20){ (7.822 x1629*ln[p]) ? (3.28109)? € = 1.088 21717-45.97470%xCamcp)) ?) inn n2

Now Probability of 10%. Polis © Es 1.088 X 10"9_(5.944x1623(en (0:1)° ) E = 1.084 X1018 ] A. Reguired eneegy is /E = 1.08481018) Palt B To find eneegy electron has a toneling probability of 1.07. - ie P=0.01 Es 1.088x1013 (5.97481023x(en (0.01))) E=1.075 x1018 J .. Required Energy E= 1.075 01018 / Palt(e) To find eneegy election has a toneling probability of 0.10% P=0.001 E- 1.08971018-(5.974x102xlen(0.001))) € 21.08781018 J :. Regueired EnergyE = 1.083 xigl85]