Question

Calculate the energy levels for n=1,2 and 3 for an electron in a potential well of width 0.25nm with inflate barriers on either side. The energies should be expressed in Kj/mol. The answers should be 580.5, 2322, and 5225 Kj/mol

Answer 1

The energy for a particle in a box are given as

here L = 0.25 nm = 2.5 X10^-10 m

For E1 where n = 1

E1 = (1^2)(6.62X10^-34Js)^2/ 8 X9.1 X10^-31kg X (2.5 X10^-10m)^2

E1 = 0.096 X10^-17J

now to find the kilojoule for 1 mol for this use Avagadro number

E = 0.096X10^-17 X6.022X1023 mole^-1

E1 = 580023.142

divide this by 1000 for kj/mole

E1 = 580.023 kJ/mole

2. Now when n=2

E2 = 4 X h^2/8 X9.1X10^-31kgX2.5X10^-10m

E2 = 0.384X10^-17

For mole^-1

E2 = 0.384 X10^-17 X6.022X10^23 =2312448 J/mole divide by 1000 = 2312.448 kJ/mole

3. when n=3

E3 = 9 Xh^2/ 8X9..1X10^-31X6.25X10^-20 = 0.864X10^-17

For per mole = 0.864X10^-17X6.022X10^23= 5203008/1000=5203.008kJ/mole