Question

An electron is confined in the ground state in a one-dimensional box of width 10-10 m. Its energy is known to be 38 eV. (a) Calculate the energy of the electron in its first and second excited states (b) Sketch the wave functions for the ground state, the first and the second excited states (c) Estimate the average force (in Newtons) exerted on the walls of the box when the electron is in the ground state. (d) Sketch the new ground state wave function after a repulsive short range potential is introduced at the centre of the box. Assume this potential to be well represented by a delta function. Justify your choice of wave function.

Answer 1

10 Given: Potential well of width (L) = 10 tom. Ground state energy (E1): 38 eu. Ans-a) We know the formula .: Kn=h2 h² 8 ml? Bret for nel le for ground state hi: zsev He need to calculate the energy of electoon in first and second excited states . : £2=4 h = 4x38 ev = 152 ev = 2.435x10 ... 3 : 913 9x 38 eu - 342 EN = 5.479 x 18 ttg

Ans.o) Fig. The wave function in a lo box for ground, first and second excited state Ans.c) He know (f)=(-00) -(-%€ (-1/6) > - e2 Lahe (!)) Here (le) = 2/2²

...(P) = -2 02 do Where do be the Bohr-radius= 5.29x10thm. e - be the charge on electron -d .6%d0