The volume of a sodium crystal = 0.1 cm 3 = 0.1*(10 -2 m) 3 = 10 -7 m 3 The span

Question

The volume of a sodium crystal = 0.1 cm3 = 0.1*(10-2 m)3 = 10-7 m3

The spanning range of 3s electron energies = 3.2 eV = 3.2*1.6*10-19 J = 5.12*10-19 J (since 1 eV = 1.6*10-19 J)

The electron concentration of sodium crystal = 2.65*1028 m-3

i.e. The no. of moles of electrons per volume = 2.65*1028 mol/m3

i.e. The no. of moles of electrons / 10-7 m3 = 2.65*1028 mol/m3

i.e. The no. of moles of electrons = 2.65*1028 mol/m3 * 10-7 m3 = 2.65*1021 mol

The average spacing between the energy levels in the 3s band =?

= 5.12*10-19 J / 2.65*1021 mol

= 1.93*10-40 J/mol

1 kJ/mol = 0.0103642688 eV/atom, i.e. 1 J/mol = 1.03643*10-5 eV/atom

Therefore, the average spacing between the energy levels in the 3s band = 1.93*10-40 * 1.03643*10-5 eV/atom

= 2*10-45 eV/atom

Explanation / Answer

4.2. Consider a crystal of sodium with a volume 0.10cm3, estimate the average spacing between the energy levels in the 3s band given that the 3s electron eneregies span a range of 3.20eV. The electron concentration of a sodium crystal is approximately 2.65 x 102s m. (You can estimate this value by yourself.)

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.