Question

An electron with total energy E = 0.1 eV is trappped in a finite square well of height 20 eV,

except for the region 0 < x < 2 nm. What is the penetration depth into the classically

forbbidden region x<0?

Answer 1

given

E = 0.1 eV

= 0.1 X 10^-19 J

h_o = 20 eV

U_o = m g h_o

= 9.1 X 10^-31 X 9.8 X 20 X 1.6 X 10^-19

= 1.426 X 10^-48 J

penetration depth = 1/k

k = ( 2 m ( U_o - E ) / $\hbar$ ² )^1/2

$\hbar$ = 2 X 6.67 X 10^-34 / 6.28

$\hbar$ = 2.124 X 10^-34

k = ( 2 X 9.1 X 10^-31 X ( 1.426 X 10^-48 - 0.1 X 1.6 X 10^-19 ) / ( 2.124 X 10^-34 )² )^1/2

k = 803417288.4

penetration depth = 1/k

penetration depth = 1/803417288.4

penetration depth = 1.2446 X 10^-9 m

or

penetration depth = 1.2446 nm