the electronic structure of atoms

New Way Chemistry for Hong Kong A-Level Book 11

The Electronic The Electronic Structure of AtomsStructure of Atoms

4.14.1 The Electromagnetic SpectrumThe Electromagnetic Spectrum

4.24.2 Deduction of Electronic Structure Deduction of Electronic Structure from Ionization Enthalpiesfrom Ionization Enthalpies

4.34.3 The Wave-mechanical Model of the The Wave-mechanical Model of the AtomAtom

4.4 Atomic Orbitals4.4 Atomic Orbitals

44


The electronic structure of atomsThe electronic structure of atoms

Niels Bohr

Bohr’s model of H atom

Chapter 4 The electronic structure of atoms (SB p.80)


The electromagnetic spectrumThe electromagnetic spectrum

c

4.1 The electromagnetic spectrum (SB p.82)

c


Continuous spectrum of white Continuous spectrum of white lightlight

Fig.4-5(a)



Line spectrum of hydrogenLine spectrum of hydrogen

Fig.4-5(b)



The emission spectrum of atomic hydrogenThe emission spectrum of atomic hydrogenUV Visible IR



Interpretation of the atomic Interpretation of the atomic hydrogen spectrumhydrogen spectrum



Bohr proposed for a hydrogen Bohr proposed for a hydrogen atom:atom:1. An electron in an atom can only exist in certai

n states characterized by definite energy levels (called quantum).

2. Different orbits have different energy levels. An orbit with higher energy is further away from the nucleus.3. When an electron jumps from a higher energy

level (of energy E1) to a lower energy level (of energy E2), the energy emitted is related to the frequency of light recorded in the emission spectrum by: E = E1 - E2 = h



How can we know the energy levels are getting closer and closer together?



E = E1 - E2 = h

Planck ’s constant

Frequency of light emitted



Emission spectrum of hydrogen

Absorption spectrum of hydrogen

dark background(photographic plate)

bright lines

bright background(photographic plate)

dark lines



Production of the absorption Production of the absorption spectrumspectrum

Absorption spectrum of hydrogen

bright background(photographic plate)

dark lines



Convergence limits and ionizationConvergence limits and ionization

What line in the H spectrum corresponds to this electron transition (n= ∞ n=1)?

What line in the H spectrum corresponds to this electron transition (n= ∞ n=1)?

Last line in the Lyman SeriesLast line in the Lyman Series

For n=∞ n=1:

H (g) H+(g) + e-




Example 4-1AExample 4-1A Example 4-1BExample 4-1B


The uniqueness of atomic emission spectraThe uniqueness of atomic emission spectra

No two elements have identical atomic spectra

atomic spectra can be used to identify unknown elements.


Check Point 4-1Check Point 4-1


4.4.22 Deduction of Deduction of

Electronic Electronic Structure from Structure from

Ionization Ionization EnthalpiesEnthalpies


Ionization enthalpyIonization enthalpy

Ionization enthalpy (ionization energy) of an atom is the energy required to remove one mole of electrons from one mole of its gaseous atoms to form one mole of gaseous positive ions.

Ionization enthalpy (ionization energy) of an atom is the energy required to remove one mole of electrons from one mole of its gaseous atoms to form one mole of gaseous positive ions.

The first ionization enthalpy

M(g) M+(g) + e- H = 1st I.E.

The second ionization enthalpy

M+(g) M2+(g) + e- H = 2nd I.E.

4.2 Deduction of electronic structure from ionization enthalpies (p.91)


Evidence of shellsEvidence of shells

shells



Evidence of sub-shellsEvidence of sub-shells

2,1

2,2

2,3

2,4

2,5

2,6

2,7

2,8 subshells




4.4.33 The Wave-The Wave-

mechanical mechanical Model of the Model of the

AtomAtom


Bohr’s atomic model and its limitationsBohr’s atomic model and its limitations

Bohr considered the electron in the H atom (a one-electron system) moves around the nucleus in circular orbits.

Basing on classical mechanics, Bohr calculated values of frequencies of light emitted for electron transitions between such ‘orbits’.

The calculated values for the frequencies of light matched with the data in the emission spectrum of H.

4.3 The Wave-mechanical model of the atom (p.94)


Bohr tried to apply similar models to atoms of other elements (many-electron system), e.g. Na atom.

Basing on classical mechanics, Bohr calculated values of frequencies of light emitted for electron transitions between such ‘orbits’.

The calculated values for the frequencies of light did NOT match with the data in the emission spectra of the elements.

The electron orbits in atoms may NOT be simple circular path.



Wave nature of electronsWave nature of electrons

A beam of electrons shows diffraction phenomenon Electrons possess wave properties

(as well as particle properties).



Wave nature of electronsWave nature of electronsSchrödinger used complex differential equations/wave fucntions to describe the wave nature of the electrons inside atoms (wave mechanic model).

The solutions to the differential equations describes the orbitals of the electrons inside the concerned atom.

An orbital is a region of space having a high probability of finding the electron.



Quantum numbersQuantum numbersElectrons in orbitals are specified with a set of numbers called Quantum Numbers:

1. Principal quantum number (n) n = 1, 2, 3, 4, …...

2. Subsidiary quantum number (l) l = 0, 1, 2, 3…, n-1 s p d f

3. Magnetic quantum number (m) m = -l, …, 0, …l

4. Spin quantum number (s) s= +½, -½

The solutions of the wave functions are the orbitals -- which are themselves equations describing the electrons.

The solutions of the wave functions are the orbitals -- which are themselves equations describing the electrons.



Principal quantum number

(n)

Subsidiary quantum

number (l)

Number of orbitals (2l+1)

Symbol of orbitals

Maximum number

of electrons

held1 0 1 1s 2

2 01

13

2s2p

26

3 012

135

3s3p3d

56

104 0

123

1357

4s4p4d4f

26

1014

8

18

32



Each orbital can accommodate 2 electrons with opposite spin.

1s

2s

2p

3s

3p

3d

4s




4.4.44Atomic OrbitAtomic Orbit

alsals


ss Orbitals Orbitals4.4 Atomic orbitals (p.98)

Graph of probability of finding an electron against distance from nucleus


ss Orbitals Orbitals4.4 Atomic orbitals (p.98)


pp Orbitals Orbitals

The shapes and orientations of 2px, 2py and 2pz orbitals

4.4 Atomic orbitals (p.100)



dd Orbitals Orbitals

The shapes and orientations of 3dxy, 3dyz, 3dx2-y2 and 3dz2 orbitals



The END


Some insects, such as bees, can see light of shorter wavelengths than humans can. What kind of

radiation do you think a bee sees?

Back


Ultraviolet radiationAnswer


What does the convergence limit in the Balmer series correspond to?

Back


The convergence limit in the Balmer series corresponds to the energy required for the transition of an electron from n =2 to n = .

Answer



Given the frequency of the convergence limit of the Lyman series of hydrogen, find the ionization enthalpy of hydrogen.

Frequency of the convergence limit = 3.29 1015 Hz

Planck constant = 6.626 10-34 J s

Avogadro constant = 6.02 1023 mol-1 Answer



Back

For one hydrogen atom,

E = h

= 6.626 10-34 J s 3.29 1015 s-1

= 2.18 10-18 J

For one mole of hydrogen atoms,

E = 2.18 10-18 J 6.02 1023 mol-1

= 1312360 J mol-1

= 1312 kJ mol-1

The ionization enthalpy of hydrogen is 1312 kJ mol-1.



The emission spectrum of atomic sodium is studied. The wavelength of the convergence limit corresponding to the ionization of a sodium atom is found. Based on this wavelength, find the ionization enthalpy of sodium.

Wavelength of the convergence limit = 242 nm

Planck constant = 6.626 10-34 J s

Avogadro constant = 6.02 1023 mol-1

Speed of light = 3 108 m s-1

1 nm = 10-9 mAnswer



Back

For one mole of sodium atoms,

E = hL

=

=

= 494486 J mol-1

= 494 kJ mol-1

The ionization enthalpy of sodium of 494 kJ mol-1.

Lhc

m 10242mol10 6.02 s m 10 3 s J 106.626

9-

123-1834



(a)The first line of the Balmer series of the emission spectrum of atomic hydrogen corresponds to the energy emitted in the transition of an electron from the third energy level to the second energy level. It has a wavelength of 656.3 nm. What is the energy difference between the second and the third energy levels?

(Planck constant = 6.626 10-34 Js, Avogadro constant = 6.02 1023 mol-1)

Answer



(a) E = hv =

E = 6.626 10-34 J s

= 3.03 10-19 J (for one electron)

For 1 mole of electrons,

E = 3.03 10-19 J 6.02 1023 mol-1

= 182406 J mol-1

= 182 kJ mol-1

λc

h

m 10656.3s m 1039

18



(b)Given that the frequency of the convergence limit corresponding to the ionization of helium is 5.29 1015 Hz, calculate the ionization enthalpy of helium.

(Planck constant = 6.626 10-34 Js, Avogadro constant = 6.02 1023 mol-1)

Answer(b) For 1 mole of helium atoms,

I.E. = hvL

= 6.626 10-34 J s 5.29 1015 s-1 6.02 1023 mol-1

= 2.11 106 J mol-1

= 2110 kJ mol-1



(c) The blue colour in fireworks is often achieved by heating copper(I) chloride (CuCl) to about 1200 oC. The compound then emits blue light with a wavelength of 450 nm. What is the energy released per copper(I) ion at the specified condition?

Answer

(c) E =

=

= 4.42 10-19 J

λhc

m 10450ms 10 3 s J 106.626

9

-1834


(d)Name the element present in the sample when the following flame colours are observed in flame tests.

(i) Golden yellow

(ii) Lilac

(iii) Brick-red

(iv) Bluish greenAnswer

(d) (i) Sodium

(ii) Potassium

(iii) Calcium

(iv) Copper

Back



(a)Given the successive ionization enthalpies of boron, plot a graph of the logarithm of successive ionization enthalpies of boron against the number of electrons removed. Comment on the graph obtained.

Successive I.E. (in kJ mol-1): 800, 2400, 3700, 25000, 32800 Answer




(a)

The first three electrons of boron are easier to be removed because they are in the outermost shell of the atom. As the fourth and fifth electrons are in the inner shell, a larger amount of energy is required to remove them.


(b) Give a rough a sketch of the logarithm of successive ionization enthalpies of potassium. Explain your sketch. Answer




(b) There are altogether 19 electrons in a potassium atom. They are in four different energy levels. The first electron is removed from the shell of the highest energy level which is the farthest from the nucleus, I.e. the fourth (outermost) shell. It is the most easiest to be removed. The second to ninth electrons are removed from the third shell, and the next eight electrons are removed from the second shell. The last two electrons with highest ionization enthalpy are removed from the first (innermost) shell of the atom. They are the most difficult to be removed.


(c)There is always a drastic increase in ionization enthalpy whenever electrons are removed from a completely filled electron shell. Explain briefly.

Answer


(c) A completely filled electron shell has extra stability. Once an electron is removed, the stable electronic configuration will be destroyed. Therefore, a larger amount of energy is required to remove an electron from such a stable electronic configuration.

Back


(a)What are the limitations of Bohr’s atomic model?

(b)Explain the term “dual nature of electrons”.

(c) For principal quantum number 4, how many sub-shells are present? What are their symbols?

Back4.3 The Wave-mechanical model of the atom (p.97)

(a) It cannot explain the more complicated spectral lines observed in emission spectra other than that of atomic hydrogen. There is no experimental evidence to prove that electrons are moving around the nucleus in fixed orbits.

(b) Electrons can behave either as particles or a wave.

(c) When n = 4, l = 0, 1, 2 and 3, there are 4 sub-shells. The symbols are 4s, 4p, 4d and 4f respectively.

Answer


(a)Distinguish between the terms orbit and orbital.

(b)Sketch the pictorial representations of an s orbital and a p orbital. What shapes are they?


(a) “Orbit” is the track or path where an electron is revolving around the nucleus. “Orbital” is a region of space in which the probability of finding an electron is very high (about 90 %).

(b) s orbital is spherical in shape whereas p orbital is dumb-bell in shape.

Answer


(c)How do the 1s and 2s orbitals differ from each other?

(d)How do the 2p orbitals differ from each other?


Answer

(c) Both 1s and 2s orbitals are spherical in shape, but the 2s orbital consists of areas of high probability known as nodal surfaces.

(d) There are three types of p orbitals. All are dumb-bell in shape. They are aligned in three different spatial orientations designated as x, y and z. Hence, the 2p orbitals are designated as 2px, 2py and 2pz.

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the electronic structure of atoms

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