Question

Classically, if you put a particle in a box, it can have Zero kinetic energy (ie the particle is not moving). But a quantum particle always has some kinetic energy. The difference between the lowest value of the potential energy and the energy of the lowest energy eigenstate is called the Zero Point Energy. Consider a 1D box that is one nanometer in length. What is the zero point energy for an electron, a proton, a methane molecule, and a gold atom in Joules

Answer 1

Electron = 6.030 × 10^-21 J.

Proton = 3.37 × 10^-23J.

Methane = 2.06 × 10^-24J.

Gold = 1.67 × 10^-25J.

Step-by-step explanation:

Without mincing words let's dive straight into the solution to the question above.

One an energy formula will be used in solving this question. This formula is given below;

Energy, E = (n^2 × h^2)/8 × m× L^2.

Where m = mass, n = number of energy level, h = planck's constant and L = length.

Therefore, for electron;

Energy, E = (6.626 × 10^−34)^2/ ( 8 × 9.1 × 10^-31 × [1 x 10^-9m]^2 =6.030× 10^-21J.

For proton;

Energy, E = (6.626 × 10^−34 )^2 / (8

× 1.626 × 10^-27 × [1 × 10^-9]^2) = 3.37 × 10^-23J.

For methane;

Energy, E = (6.626 × 10^-34) ^2/ ( 8 × 2.66 × 10^-26 × [1 × 10^-9]^2 = 2.06 × 10^-24J.

For Gold;

Energy, E =( 6.626 × 10^−34)^2 / ( 8 × 3.27 × 10^-25 × [ 1 × 10^-9]^2) = 1.67 × 10^-25J.

NB: n = 1 = Zero Point Energy.