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Unformatted text preview: y , L z are the lengths of the sides of the box Therefore, for a state described by (1, 2, 1), we have p x = h/L x , p y = 2h/L y , p z = h/L z and E = h 2 /2m x (1/L x 2 + 4/L y 2 + 1/L z 2 ) which are evaluated as below: p x = 6.626x10-34 Js/1x10-9 m = 6.626x10-25 kgms-1 p y = 2 x 6.626x10-34 Js/1.3x10-9 m = 1.019x10-24 kgms-1 p z = 6.626x10-34 Js/1.5x10-9 m = 4.417x10-25 kgms-1 E = (6.626x10-34 Js) 2 /(2 x 9.1x10-31 ) x 1/10-18 (1/1 2 + 4/1.3 2 + 1/1.5 2 ) = 9.194x10-19 J E = 5.739eV (b) On the other hand, if we had an infinite potential well, using boundary condition for it: p x = 6.626x10-34 Js/1x10-9 m/2 = 3.313x10-25 kgms-1 p y = 2 x 6.626x10-34 Js/1.3x10-9 m/2 = 0.51x10-24 kgms-1 p z = 6.626x10-34 Js/1.5x10-9 m /2= 2.209x10-25 kgms-1 E=(6.626x10-34 Js) 2 /(8 x 9.1x10-31 ) x 1/10-18 (1/1 2 + 4/1.3 2 + 1/1.5 2 ) = 2.3x10-19 J = 1.43eV...
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- Spring '10