An electron is confined in a 3-dimensional rectangular box (v = 0 inside and v = [infinity] outside) with sides l = 4 nm, 4 nm and 5 nm. what minimum energy e must a photon have in order to excite the electron out of its ground state. (the electron absorbs the photon.)

0.045 eV

Explanation:

The energy of the electron which is confined in the three dimensional rectangular box is,

Here for the ground state all the values of n will be,

And according to question,

Therefore, ground state energy will be,

Now the minimum energy required to excite the electron from its ground state is,

So for first excited state there will be 3 possibilities are (1,1,2), (2,1,1), (1,2,1). So in these three cases minimum energy case is (1,1,2)

So minimum energy for first excited state is,

Sop the minimum energy will be,

Therefore minimum energy required to excite electron from its ground state is 0.045 eV

6 cos 34, 6 sin 34 trig