An electron is in a one-dimensional box of length 0.5 nm.The energy of this electron in its first excited state is
A)37.6 eV
B)27.4 eV
C)13.5 eV
D)6.02 eV
E)1.50 eV

Question

Quizplus · Accepted Answer

The energy levels of an electron in a one-dimensional box are given by the equation:

E = (n²h²) / (8mL²)

where n is the energy level (n = 1 for the first excited state), h is Planck's constant, m is the mass of the electron, and L is the length of the box.

Substituting the given values, we get:

E = (1² x 6.626 x 10^-34 J s)^2 / (8 x 9.11 x 10^-31 kg x 0.5 x 10^-9 m)^2

E = 13.5 eV (rounded to one decimal place)

Therefore, the correct answer is C.

An Electron Is in a One-Dimensional Box of Length 0