CHAPTER 3- Quantum Theory and Electronic Structure of Atoms
Prof Kweyete
1. Show your calculations for the followings;
a) Frequency(ν) of radiation of light whose wavelength(λ) is 460 nm.
ν = c/λ = (3.0 x 108 m/s)/(460 x 10-9m) = 6.5 x 1014 s-1
b) energy of a photon of frequency of 5.20x1011 s-1.
E = hν = (6.63 x 10-34J-s)(5.20 x 1011 s-1) = 3.45 x 10-22J
c) wavelength of radiation with photons of energy 3.70x10-17 J.
E = (hc)/λ ; λ = (hc)/E = (6.63x10-34J-s)(3.0x108m/s)/3.7x10-17J= 5.38x10-9m
d) final transition from n=2 state of hydrogen atom if the wavelength of
light
corresponding to this transition is 486 nm. ΔE = -2.18x10-18J(1/n2f - 1/n2i)
ΔE= (hc)/λ = -2.18x10-18J(1/n2f-1/22) = (6.63x10-34)(3.0x108)/486x10-9 = nf = 4
2. (a) What is the velocity of a neutron( mN = 1.67x10-24 g) which exhibit a
wavelength of 580 nm?
λ = h/(mv) = 580x10-9m = (6.63 x 10-34J-s)/(1.67x10-27kg)(v); v = 0.68 m/s
(b) Calculate the wavelength of an electron ( me = 9.11x10-28 g) which
travels at
velocity of 500.0 m/s.
λ = h/mv = (6.63x10-34J-s)/(9.11 x 10-31kg)(500.0 m/s) = 1.46 x 10-6m
3. Consider the third energy level (third shell), n=3;
a) predict the number of orbitals (subshells) and label each orbital.
Orbitals = n2 = 9 orbitals => s, Px, Py, Pz, dxy, dxz, dyz, dx2-y2, dz2
b) determine the maximum number of electrons.
Maximum # = 2n2 = 18 electrons
c) identify l and ml values for this energy level.
For l=0, ml =0; For l = 1, ml = -1, 0, 1; For l = 2, ml = -2, -1 , 0, 1, 2
4. Determine the following quantities;
a) total number of electrons in n=4.
Number of elecrons = 2n2 = 32
b) total number of electrons in n=3 , l=2.
3d orbitals => 10 electrons
c) total number of electrons in n=1, l=0, m=0.
1s orbital => 2 electrons
d) total number of electrons in n=1,l=0, m=0, s=+1/2.
1s1 designation => 1 electron
e) total number of electrons in 2p orbitals.
2p orbitals => 6 electrons
f) total number of orbitals in 3d.
5 orbitals in d subshells
g) orbital designation for n=4, l=3.
4f orbital designation
h) orbital designation for n=1, l=1. Does not apply
i) orbital designation for n=3, l=1, m=-2. Does not apply
j) orbital designation for n=2, l=1, m=-1, s=+1/2.
2p1x
5. Circle the orbital with highest energy( least effective nuclear charge);
(a) 1s,2s,3s
(b) 2s,2p,3p
(c) 3d,2p,2s
(d) 4s,4p, 4f
6. Consider the following atoms and ions; Cr, Cr3+, Bra) write electron configuration for Br[Ar]4s23d104p6 = [Kr]
b) write core configuration Cr3+
[Ar]3d3
c) draw energy diagram representation for Cr
[↑ ] [↑ ][↑ ][↑ ][↑ ][↑ ]
d)determine the total number of unpaired electrons in Cr
6 unpaired electrons
e) identify Cr3+ as paramagnetic or diamagnetic
paramagnetic
7. Consider the following atoms and ions; Cl- , Mg, P, K+ , Ce
a) which one is an example of ns2 family? Mg
b) which one is an example of p-block element? Cl, P
c) which is(are) isoelectronic with Argon? Cl-, K+
d) which is an example of alkaline earth metal? Mg
e) which one has outer shell configuration of ns2p3? P
f) which one has core configuration [Ne] 3s2? Mg
h) which one is an example of f-block element? Ce
i) which one is d-block element? none
8. Identify the following as excited state (ES) or ground
state (GS);
a)1s2 2s2 2p2 (GS) b)1s2 2s2 2p6 3s1 3p6 (ES)
(GS)
d)1s2 2s1 2p3 (ES) e) 1s2 2s2 2p3 (GS)
c)1s2 2s2 2p6 3s2 3p64s1 3d10
f) 1s1 2s2 (ES)
9. A yellow light (f= 5.09x1014 s-1) emits 8.43x10-18 J energy for each pulse.
How
many quanta of energy are in each pulse deposits?
(Hint: first calculate the energy of one quantum of this frequency)
E = hν = (6.63 x 10-34J-s)(5.09 x 1014s-1) = 3.37 x 10-19J/quantum
8.43 x 10-18J ÷ 3.37 x 10-19J/quantum = 25 quanta
10. Identify the isoelectronic pairs in each set.
a) Na+1 and Ne
b) F- and S2-
c) Ca2+ and K+
d) Cl- and Ne