EMISSION AND ABSORPTION SPECTRUM - … · Describing the emission and absorption spectrum of ... Why do electrons not ... charges should emit EM radiation

EMISSION AND ABSORPTION SPECTRUM

© cgrahamphysics.com 2015

Essential idea: In the microscopic world energy is discrete.

Nature of science: Accidental discovery: Radioactivity was discovered by accident when Becquerel developed photographic film that had accidentally been exposed to radiation from radioactive rocks. The marks on the photographic film seen by Becquerel probably would not lead to anything further for most people. What Becquerel did was to correlate the presence of the marks with the presence of the radioactive rocks and investigate the situation further.

Topic 7: Atomic, nuclear and particle physics 7.1 – Discrete energy and radioactivity


Guidance: • Students will be required to solve problems on

radioactive decay involving only integral numbers of half-lives

• Students will be expected to include the neutrino and antineutrino in beta decay equations

Data booklet reference: • E = hf • λ = hc / E



International-mindedness: • The geopolitics of the past 60+ years have been

greatly influenced by the existence of nuclear weapons

Theory of knowledge: • The role of luck/serendipity in successful scientific

discovery is almost inevitably accompanied by a scientifically curious mind that will pursue the outcome of the “lucky” event. To what extent might scientific discoveries that have been described as being the result of luck actually be better described as being the result of reason or intuition?



CONTINUOUS SPECTRUM OF WHITE LIGHT

When light is incident on a prism, a continuous spectrum of all visible colors is produced


Describing the emission and absorption spectrum of common gases •When a gas in a tube at low pressure is subjected to a voltage, the gas ionizes, and emits light.



GLASS DISCHARGE TUBE •  When an electric current is passed through a glass tube that

contains hydrogen gas at low pressure the tube gives off blue light.

•  When this light is passed through a prism four narrow bands of bright light are observed against a black background.

Not continuous emission line spectrum


Describing the emission and absorption spectrum of common gases •We can analyze that light by looking at it through a spectroscope. •A spectroscope acts similar to a prism, in that it separates the incident light into its constituent wavelengths. •For example, heated barium gas will produce an emission spectrum that looks like this:

•An emission spectrum is an elemental fingerprint.

400 450 500 550 600 650 700 750

λ / ×10-9 m (λ / nm)



EMISSION SPECTRUM

All elements in gaseous state give rise to a line spectrum that is characteristic of a particular element Each element can be identified by its emission spectrum Astronomers are able to determine elements present at the surface of stars



ABSORPTION SPECTRUM Spectra can be categorized by either emission or absorption spectra Absorption spectra consists of bright continuous spectrum covering full range of visible colors with dark lines where the element absorbs light


RELATIONSHIP BETWEEN SPECTRA

Dark lines fall exactly at same position as bright lines on an emission spectrum for the same element


NIELS BOHR (1914)

Why do electrons not crash into nucleus? Why is the nucleus stable and does not fly apart due to Coulomb repulsion?


LIMITATIONS OF THE MODEL

Electron around the nucleus are accelerating à they are changing velocity because they change direction EM theory predicts accelerating charges should emit EM radiation They should lose energy and crush into the nucleus Satellites in Earth’s orbit lose energy due to friction As radius of orbit decreases, they crash to Earth


BUT…. Electrons do not crush into nucleus Orbits have constant radius

How could the nucleus be stable and not fly apart due to Coulomb repulsion? Why does the atomic weight fluctuates? (Neon for example fluctuates between 20 and 22 amu) © cgrahamphysics.com 2015

MAX PLANCK (1904)

Energy of vibrating molecules can only exist in discrete amounts or quanta


ALBERT EINSTEIN (1905)

Light consists of small packets of energy called photons. Each photon has energy E = hf h = Planck’s constant = 6.6x 10↑−34 Js


BOHR’S POSTULATES

Electrons can only exist in certain orbits Energy in orbits is stable and constant Radii of orbits is stable and constant

Orbital radius and total energy of orbit are quantized Electrons only exist at certain energy levels

Electrons in these orbits do not radiate energy constantly They stay at the lowest possible energy level They move up only if they obtain energy from some source à Heated à subjected to electrical discharge


ENERGY LEVELS Electrons move from ground state (unexcited) to a higher energy level

Atom is said to be excited

An electron must absorb an amount of energy exactly equal to the difference in energy between the levels à absorption spectrum is continuous

When excited, electrons become unstable, fall back to ground state and emit a photon à emission spectrum is discrete

Evidence for discrete

energy levels in atom


GROUND STATE In the ground state, electrons are closest to nucleus

The bigger the quantum jump, the higher the energy and frequency of the emitted photons

Biggest jump, most energy, smallest λ

Smallest jump, least energy, largest λ


ENERGY LEVELS Each photon has an energy of E=hf Atomic energy levels are not equally spaced

Absorbing energy E the electrons will move up a level, emitting a photon of the same energy E when they fall down to ground state

But: emitted photon will not

necessarily be in same direction

as incident radiation

Sharp drop in intensity


ENERGY RELATIONSHIP

𝐸 = ℎ𝑓 ↔𝒇= 𝑬/𝒉  𝒗=λ𝒇 ↔𝒇= 𝒗/λ  𝑬/𝒉 = 𝒗/λ 

Energy is directly proportional to velocity and inversely proportional to wavelength


EXAMPLE

Find the photon energy of the red coloured line in the hydrogen emission spectrum with λ = 656nm Solution 𝑬= 𝒉𝒗/λ 

𝑬=6.6x10↑−34 3× 10↑8 /656× 10↑−9  =3.0×10↑−19 𝐽

𝑬= 3.0× 10↑−19 /𝟏.𝟔× 10↑−19  =𝟏.𝟖𝟕𝟓~𝟏.𝟖𝟖𝐞𝐕

Change to eV


PRACTICE: Which one of the following provides direct evidence for the existence of discrete energy levels in an atom? A. The continuous spectrum of the light emitted by a white hot metal. B. The line emission spectrum of a gas at low pressure. C. The emission of gamma radiation from radioactive atoms. D. The ionization of gas atoms when bombarded by alpha particles. SOLUTION: •Just pay attention!

Discrete energy and discrete energy levels •Discrete means discontinuous, or separated.



PRACTICE: A spectroscopic examination of glowing hydrogen shows the presence of a 434 nm blue emission line. (a) What is its frequency?

SOLUTION: •Use c = λf where c = 3.00×108 m s-1

and λ = 434 ×10-9 m: • 3.00×108 = (434×10-9)f f = 3.00×108 / 434×10-9 = 6.91×1014 Hz.

Solving problems involving atomic spectra



PRACTICE: A spectroscopic examination of glowing hydrogen shows the presence of a 434 nm blue emission line. (b) What is the energy (in J and eV) of each of its blue- light photons? SOLUTION: Use E = hf: • E = (6.63×10-34)(6.91×1014) E = 4.58×10-19 J. E = (4.58×10-19 J)(1 eV/ 4.58×10-19 J) E = 2.86 eV.

Solving problems involving atomic spectra



Documents

EMISSION AND ABSORPTION SPECTRUM - … · Describing the emission and absorption spectrum of ... Why do electrons not ... charges should emit EM radiation