Question

An electron is bound in one dimensonal infinite well, the first three excited state energy
values in terms of the ground state energy

Answer 1

Explanation:

3.     An electron is bound in one-dimensional infinite well of width 1 × 10–10 m. Find the energy values in the ground state and first two excited states

Answer 2

In a one dimensional infinite well, the first three excited state energy values in terms of the ground state energy of an electron are as follows;

If 'L' is the width of the one dimensional infinite well, then the energy of the nth excited energy state is;

$E_{n}$ = ( $n^{2}$$h^{2}$ ) / 8m$L^{2}$ , where 'h' is the Planck's constant and 'm' is the mass of the electron.

$E_{n}$ = ($n^{2}$/ $L^{2}$) (6.038 x $10^{-38}$) J

Ground state n = 1

Ground state energy $E_{1}$ = [(6.038 x $10^{-38}$) / $L^{2}$]J

First excited state       $E_{2}$ = $2^{2}$ $E_{1}$ = [(2.415 x $10^{-37}$) / $L^{2}$]J

Second excited state $E_{3}$ = $3^{2}$ $E_{1}$ = [(5.432 x $10^{-37}$) / $L^{2}$]J

Third excited state     $E_{4}$ = $4^{2}$ $E_{1}$ = [(9.66 x $10^{-37}$) / $L^{2}$]J