5. Assume that a microwave oven operates at a frequency of 1.00 x 1011 s-1. (a) What is the wavelength
of this radiation in meters? (b) What is the energy in Joules per photon? (c) What is the energy per mole
of photons?
(a) λ=c/ν = 2.998x108m/s /1.00x1011 s-1= 3.00x10-3
(b) E=hv= (2.626x10-34 J*s)x(1.00x1011 s-1) = 6.63x10-23 J for one photon
(c) (6.63x10-23 J/1 photon)x(6.022x1023 photons/ 1 mol photons)= 39.9 J/mol
6. When light with a wavelength of 58.5 nm strikes the surface of tin metal, electrons are ejected with a
maximum kinetic energy of 2.69 x 10-18 J. What is the binding energy of these electrons to the metal?
The binding energy is related to the energy of a photon:
E= Binding E + Kinetic E.
Calculate the energy of the photon with the wavelength and then find the binding energy using the
kinetic energy given.
Ephoton= hc/λ = (2.626x10-34 J*s)(3.0x108 m/s) / (58.5nm*1x10-9m/ 1nm) = 3.40 x 10-18 J/photon.
Binding E= 3.40 x 10-18 J – 2.69x10-18J= 7.1x10-19 J
7. A mercury atom emits light at many wavelengths, two of which are at 435.8 and 546.1 nm. Both of
these transitions are to the same final state. (a) what is the energy difference between the two states
for each transition? (b) if a transition between the two higher energy states could be observed, what
would be the frequency of the light?
DO ON YOUR OWN
9. A particular orbital n=4 and l=2. What must this orbital be? (a) 3p (b) 4p (c) 5d (d) 4d
The secondary quantum number, l, represents the shape of the sub-shell and l=2 is a d subshell. The
energy level is 4 (n=4) so it must be a d4 orbital.
10. What is the maximum number of electrons in an atom that can have the following quantum
numbers? (a) n=2 (b) n=3 and l=1 (c) n=3, l=1, ml=0
Electron capacity in energy levels = 2n2
(a) 2(2)2=8 electrons can have n=2, 8 electrons
(b) 2(3)2=18 electrons can have n=3 but only 6 of these can have l=1 (a p-subshell), 6 electrons
(c) only 2 of the electrons in the 3p subshell can be in the ml =0 orbital, 2 electrons