Question

Calculate the energy of an electron with mass 9.109*10^-31 kg confined in a two-dimensional box with side length 1.50 nm.

a) 2.44 x 10^-18 J
b) 4.89 x 10^-18 J
c) 7.33 x 10^-18 J
d) 9.78 x 10^-18 J

Answer 1

To calculate the energy of an electron confined in a two-dimensional box, use the equation E = (h^2 * n^2)/(8 * m * L^2), where h is the Planck constant, n is the quantum number, m is the mass of the electron, and L is the length of the side of the box.

Step-by-step explanation:

To calculate the energy of an electron confined in a two-dimensional box, we can use the equation for the energy of a particle in a box:

E = (h^2 * n^2)/(8 * m * L^2)

where h is the Planck constant, n is the quantum number (1, 2, 3, ...), m is the mass of the electron, and L is the length of the side of the box.

Plugging in the values given, we have:

E = (6.626 x 10^-34 J.s)^2 * (1^2)/(8 * 9.109 x 10^-31 kg * (1.50 x 10^-9 m)^2)

Solving this equation gives us the energy of the electron as approximately 2.44 x 10^-18 J.