Question

i got the first part, its just the rest

Part Il: Quantum Mechanics Problems 1) An electron is accelerated through a voltage of 100 V Thinking of it as a wave, what is its wavelength, in nm? (This is called the de Broglie" wavelength.) VpY Vahe .e.AV 6.626x1034 8(2)(9.1x10-3216410-19) (100) = 0.12.3 2) A photon has the same wavelength as this electron. In what part of the spectrum is this photon? What is the energy, in J and in eV, of the photon? 3) If you trap an electron in a 0.25-nm-long box, what are the first 3 possible energy states, in eV? 4) For the electron trapped in a 0.25-nm-long box, what are the 3 lowest photon energies, in eV?

Answer 1

Part-II Quantum Mechanics Problems. Valoov a=? 2= 4 = mer J2x9.110-31X16X10-19 x 100 [a=0.123rm] = 6.6 x70-34 Photon = "electron = 2.426 X 10-12 SO 14 ] - = 8.162 X 10 Echv=hc-16.6 X10 (3X10 12.426 X10-12) E = 8. 162x10-147 E = 510125 ev) or E = 5.10X105 ev] ② width of long box, a = 0.25mm ſ oss En = n2 2²² amaz fo-n25 x²x61.058 10-342 L 2 X 9.1X10-31 x(0.25X10-9) En = m? [ 9.566 X10'S] 1 En = n² [5.979 X 10" ev n=1 Ground state E = 5.9198104 en/

• n=2 , First Excited State E, = (2) [5.979X104] ev TE2 = 23.916X104ev) • n = 3, 2nd Exu'ted state Ez = (3)? [ 5.979 X 1047 ev Ez = 53.811x1046v 7 © lowest photon Energy AE, - E -E, = [(272-(02) [5.979 x1o4ev] AE, = (3) (5.919X104 eV] Ei= 17.937 X10'ev . En = n² (5.979810") er DE = E3-Ez DE, = {(3)-(22) (5.919x109ev) [DE, = 29.895 X109ev DE = Eu - E3 2E2 = 14)2-1312) (5.919 xio'ev) DEZ = 41.853% 104 ev