PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

PA1140

Waves and Quanta

Unit 4: Atoms and Nuclei

Dr Matt Burleigh (S4)

Tipler, Chapters 36 & 40

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

• http://www.star.le.ac.uk/mbu/lectures.html

Lecture course slides can be seen at:

•Bohr theory •Radioactivity, fission and fusion•Atomic size and shape•Mass and binding energy

Unit 4Atoms and Nuclei (chapters 36 &

40).

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

• The 100 odd different stable nuclei make up the matter around us• Their physical and chemical properties are determined by laws which govern the

behaviour of the electrons surrounding the nucleus• The arrangement of the electrons determines their emission and absorption line

characteristics• The spacings and wavelengths of the lines are characteristic of each element

This is an interacting binary star system called a cataclysmic variable. The small white dwarf star is pulling matter off its brown dwarf companion, down its magnetic field lines onto its surface. The absorption lines in the spectrum (left) are H gas in the white dwarf atmosphere. The H emission lines are from the bright spot where the accreting matter hits the white dwarf.

Emission lines

Absorption lines

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

Atomic Spectra

Ch. 36

In 1884 Balmer found the wavelengths of lines in the visible spectrum of H can be represented by

Where m=3,4,5….

Rydberg & Ritz gave a more general expression applicable to the spectra of other elements

Where n1 & n2 are integers and n1 > n2. R is the Rydberg constant

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

• The Rydberg-Ritz formula works mathematically, but why?• In 1913 Niels Bohr proposed a pre-QM model to explain the spectra

emitted by H atoms• In this theory electrons are considered to be point objects in orbit

around the nucleus• It gives a 1st order explanation of the spectral lines, & remains a

useful treatment of electron behaviour• Next year you will gain enough QM knowledge to see how the true

quantum description of such systems works

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

The Bohr atom

Ch. 36

The centripetal force acting on the orbiting electron is the electrostatic force of attraction (Coulomb force)

(1)

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

• The energy of the orbiting electron is thus:

• But classical EM theory says such an atom is unstable, bcse the electron must accelerate when moving in a circle & radiate EM energy

• Thus the orbit would quickly collapse as the electron spiralled into the nucleus as energy is radiated away

• Bohr proposed a way out of this difficulty with a set of postulates • He had no proof, just a starting point of assumptions!

(2)

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

Bohr’s postulates(1) Bohr proposed that certain “magical” circular orbits existed, called

“stationary states”, which did not radiate, and that electrons could only exist in these states, with radiation occurring when they made the transition from one to the other.

(2) He also postulated that the frequency of the radiation from spectral lines was determined by energy conservation during transitions from one stationary state to the other. i.e.

Combining this with the expression for electron energy gives

(3). Trial and error led Bohr to his third postulate, that angular momentum is quantized, specifically that

(3)

From E=hf, where h is Planck’s constant

n is the quantum number of the state

PA 1140 Waves and Quanta Unit 4: Atoms and Nuclei

Where the Rydberg constant, R, is:

Radius of orbit:

Frequency of line:

(4)

Energy of orbit n

so

&