The ground state energy of an electron in a one-dimensional box is given by the formula:
E = (n^2 * h^2) / (8 * m * L^2)
Where:
E = energy
n = quantum number (positive integer)
h = Planck's constant (6.626 x 10^-34 Js)
m = mass of the electron (9.11 x 10^-31 kg)
L = length of the box
Comparing the two scenarios:
- In the first case, the box has a length of 10^-6m. So, L = 10^-6m.
- In the second case, the box has a height of 10^-6m. So, L = 10^-6m as well.
In both cases, the only variable that is different is the height of the box. Since the formula for energy is inversely proportional to the square of the length of the box, the box with the smaller length (10^-6m) will have the lower ground state energy for an electron.
Therefore, the electron trapped in a one-dimensional box of length 10^-6m will have the lowest ground state energy.
which has the lowest ground state energy, an electron trapped in a one-dimensional box of height 10^-6m or one with length 10^-6m
1 answer