Question

What is the lowest energy level, in electron volts (eV), of an electron in a one-dimensional box of atom size, 0.397 nm in width? Number Find the lowest energy level, in units of a million electron volts (MeV), of a proton in a one-dimensional box of nucleus size, with a width of 1.01 x10-4 m? Number MeV

Answer 1

Here, we need to use the equation for one dimensional box

E = n²h² / 8mL²

L is width of box, m is mass of charge, h is Planck's constant

SO,

for electron, lowest energy energy, n = 1

E = 6.63e-34² / 8 * 9.1e-31 * 0.397e-9²

E = 3.831e-19 J

E = 2.39 eV

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For proton,

E = 6.63e-34² / 8 * 1.67e-27 * 1.01e-14²

E = 2.0128 MeV