Question

• The lowest energy of an electron
constrained to move in one
dimensional potential box of length
0.1 nm is eV. (Mass of electron =
9.1 x 10^-31 kg, Plancks Constant h:
6.63 x 10^-34 Js)​

Answer 1

We have find the lowest energy of an electron constrained to move in one dimensional potential box of length 0.1 nm in eV.

energy of an electron in a box of length L is given by,

$\bf E=\frac{n^2h^2}{8mL^2}$

where, n is energy level , h is Plank's constant , m is mass of electron and L is length of box.

To find lowest energy of an electron, n = 1

h = 6.63 × 10⁻³⁴ Js

m = 9.1 × 10⁻³¹ Kg

L = 0.1 nm = 10⁻¹⁰ m

∴ $E=\frac{1^2\times(6.63\times10^{-34})^2}{8\times9.1\times10^{-31}\times(10^{-10})^2}$

= 6.038 × 10⁻¹⁸ J

Therefore the lowest energy of an electron constrained to move in one dimensional potential box is 6.038 × 10⁻¹⁸