The Atomic Spectrum of Hydrogen, Orbitals and spdf Notation

PresenterG. Delapenha

Lesson 4

Old Theory

+n=2

n=1

n=3

n= infinity

nucleus

Energy Levels

Highest energy level

Lowest energy level

Radiowaves

Microwaves

Infrared .

Ultra-violet

X-Rays

Visible Light

Electromagnetic Spectrum

Increasing frequency

Increasing wavelength

(Visible region)

Electronic transition

Is when an electron moves from one energy level to another. example

+n= 1

n=2

Energy

Absorption Spectra

+

When an atom is excited by absorbing energy, an electron jumps up to a higher energy level.

nucleus

Energy

n= 1

n=2

, Example heat or electricity

Absorption Spectra cont’dAn absorption spectrum occurs when the electron in the lowest level (ground state) is provided with energy to lift it to higher energy levels.

Spectrum of hydrogen

Emission Spectra

+

Energy is emitted when an electron falls from a higher to a lower energy level.

nucleus

Radiation

Emission spectra arise when electrons, having been excited to higher energy levels, return to lower ones and give out energy

Balmer, was the first to notice this effect and gave his name to the spectral series resulting from transitions back to the second energy level (n=2). This is in the visible region.

Emission Spectra cont’d

Lyman series is a spectral series resulting from transitions back to the first energy level (n=1). This is in the ultraviolet region.

Paschen series is a spectral series resulting from transitions back to the third energy level (n=3). This is in the infrared region.

See previous slide for illustration

Convergence limit• Is the frequency at which the spectral lines come

together at the highest energy level (n = ∞)• It corresponds to the point at which ionization

takes place if an electron is excited beyond this level

n=1

n=2

n=3

n=4

…

n= ∞

Convergence limit

Electron is lost from atom!

An

Line spectrum of various elements

Note

All substances give emission spectra when they are excited in some way either by heat or the passage of an electric current.

A closer look at an electronic transition

ener

gy

En=2

En=1

The small amount of energy absorbed or emitted when an electron undergoes a transition between energy levels is called a quantum ( plural = quanta) of energy

quantum

absorption

emission

ΔE

Quantum, ΔEQuantum, ΔE = En=2 - En=1 = h

E = h

Introduced by Max Planck (1900)

Planck’s EquationWhere h = Planck’s constant (6.63 x 10-34Js)n = frequency of radiationC = speed of light = wavelength

V is a Greek letter called ‘nu’

𝑬=𝒉𝒄𝝀

Subshells

• Bohr’s model explains the emission spectrum of the H atom in terms of electronic transition between shells.

• The emission spectrum of the other elements eg sodium(Na) is much more complex. This could not be explained by the Bohr’s model

• To explain the spectrum there must be subdivisions of the Bohr shells, called subshells.

Subshells cont’d

• It was found that:

shell Number of subshells

subshells

n=1 1 sn=2 2 s, pn=3 3 s, p, dn=4 4 s, p, d, f

New Theory

Orbital

Quantum Numbers

Four(4) quantum numbers determine the orbitals (not orbits) and gives information about energy levels available to an atom.1. Principal quantum number, n

n = 1, 2, 3, 4, …, ∞ (shells)2. Subsidiary quantum number, l

l = 0, 1, 2, 3, …, (n-1) (subshells)3. Magnetic quantum number, m

m = …, -1, 0, 1, 2, …4. Spin quantum number, s

s = ± ½

Each subshell is made up of a fixed number of orbitals

Subsidiary quantum number, l

Subshell (code letter)

Number of

Orbitals

Maximum number of electrons

0 s 1 2

1 p 3 6

2 d 5 10

3 f 7 14

Note: Each orbital has the same name as its subshell.

s atomic Orbital• Is spherically symmetric about the nucleus• There is one (1) s orbital for each principal quantum number

zy

x

p Atomic Orbitals• Pairs of ‘dumb-bells’ aligned along the x, y, z axis at 90 to each other• There are three(3) p orbitals for each principal quantum number from n =

2 onwards denoted by 2p, 3p, 4p, etc• Can hold a maximum 6 electrons, 2 in each p orbital.

zy

x

zy

xz

y

x

Shapes of d orbitals and f orbitals

• More complex and beyond the scope of this course.

Energy Levels

Rules for Filling Energy LevelsThe Building-up (or Aufbau) Principle

Pauli Exclusion Principle

Hund’s Rule

Spin Electrons act as if they were spinning around an axis, in much the same way that the earth spins. This spin can have two orientations, denoted as up and down

up down

Filling Order

Example1: write the Electronic Configuration of Oxygen using spdf notation.

𝟏 𝒔𝟐𝟐𝒔𝟐𝟐𝒑𝒙𝟐𝟐𝒑𝒚

𝟏 𝟐𝒑𝒛𝟏

Incr

easi

ng E

nerg

y

or 1s22s22p4

Atomic no. of O = 8

Remember rules for filling orbitals!

Example1: Write the Electronic Configuration of calcium using spdf notation.

𝟏 𝒔𝟐𝟐𝒔𝟐𝟐𝒑❑𝟔𝟑 𝒔❑

𝟐 𝟑𝒑❑𝟔 𝟒 𝒔❑

𝟐

Incr

easi

ng E

nerg

y

or

Atomic no. of Ca = 20

𝟏 𝒔𝟐𝟐𝒔𝟐𝟐𝒑❑𝟔𝟑 𝒔❑

𝟐 𝟑𝒑❑𝟔 𝟒 𝒔❑

𝟐 or

likewise

1s22s22p63s23px23py

23pz1

Can be written as

[Ne]3s23px23py

23pz1

e.c. of Argon (Ar)Shortened form of e.c. of Calcium (Ca)

Neon (Ne) Shortened form of e.c. of Chlorine (Cl)

Ca

Cl

Activities

1. Write the electronic configuration of the first 20

elements in the periodic table using spdf notation.

Use the table in the next slide.

2. Illustrate the electronic configuration of phosphorus

and potassium using boxes to show the different

energy levels and using spdf notation