The energy level of an electron trapped in a one-dimensional box is directly related to the size of the box. As the length of the box increases, the energy levels of the electron also increase.
In a one-dimensional box, the energy levels for electrons are quantized, meaning they can only take on discrete values. The energy levels are given by the equation:
E_n = (n^2 * h^2) / (8 * m * L^2)
where E_n is the energy level, n is the quantum number (an integer), h is the Planck constant, m is the mass of the electron, and L is the length of the box.
As the length of the box increases, the denominator in the equation for the energy levels also increases. This results in higher energy levels for the electron, meaning that the electron has more energy when it is confined in a larger box.
In summary, as the length of the box increases, the energy levels for an electron trapped in a one-dimensional box also increase. This relationship between the size of the box and the energy levels is an important concept in quantum mechanics and has implications for the behavior of electrons in different confinement geometries.
discuss what happen to the energy level for an electron trapped in a one dimensional box as the length of the box increases
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1 answer