Question

An electron (restricted to one dimension) is trapped between two rigid walls 1.40 nm apart. The electron's energy is approximately 19 eV. (a) What is the quantum number n for the energy state that the electron occupies

Answer 1

The quantum number of the energy state occupied by the electron is 10.

The given parameters;

• distance between the two rigid walls, L = 1.4 nm
• energy of the electron, E = 19 eV

The quantum number of the electron is calculated as follows;

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

where;

• h is Planck's constant = 6.626 x 10⁻³⁴ Js
• m is mass of electron = 9.11 x 10⁻³¹ kg
• E is the energy of the electron = 19 x 1.602 x 10⁻¹⁹ J
• n is the quantum number of the energy state occupied by the electron.

$n^2 = \frac{8mL^2E_n }{h^2} \\\\n = \sqrt{\frac{8(9.11\times 10^{-31} )(1.4 \times 10^{-9})^2 (19\times 1.602 \times 10^{-19}) }{(6.626\times 10^{-34})2} } \\\\n \approx 10$

Thus, the quantum number of the energy state occupied by the electron is 10.

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