Quantum Nature of radiation

Book page 476 - 477

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Black body radiation • The perfect emitter or absorber of radiation is a black body

• The radiation from a perfect theoretical emitter is called black body radiation

Emission:

• Only depends on temperature

• At any given temperature there will be a range of emitted wavelengths and frequencies

• The Rayleigh – Jeans law predicted: 𝐼∞𝑓2

• This lead to the UV catastrophe following classical mechanics

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Predicted outcome was not observed

• According to Maxwell, radiation originates from oscillating charges in the atoms of the material

• As T ↑, f of oscillations ↑ • f of radiated light should ↑ not observed • Does not agree in UV portion of spectrum – UV catastrophe

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Quantum solution

Planck proposed

• Vibrating molecules only vibrate with specific energies

• Energy is radiated not in continuous form but in bundles called quanta

• Each quanta consists of photons with energy E = hf where E = photon energy (J) h = Planck’s constant = 6.63 × 10−34𝐽𝑠−1 f = frequency (Hz)

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Quantum nature of radiation • Under certain conditions, when UV light is shone on a metal

surface, electrons are emitted from the surface

• This was called photoelectric effect

• Emitted electrons are called photoelectrons

• It was assumed, if light is a wave, that

• Electrons are only emitted if they have enough energy

• This should only depend on the intensity of incident light

This was not observed 1 - Photoelectric !.mpg

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Observation • For any metal, electrons are only ejected if the frequency of

the incident light f is above a threshold frequency 𝑓0

• Weak UV light can emit electrons, intense IR light cannot, even if it delivers more energy per second

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…continued • 𝑓0 depends on metal and is lower for more reactive metals this would mean more electrons are ejected for the same frequency in the more reactive metal

• 2 - photoelectric.jar

• Below 𝑓0 no electrons are emitted

• Above 𝑓0 the KE of the ejected electrons depends only on the frequency of incident light

• The number of electrons emitted depends on the intensity of incident light

• Questions: What will happen to the rate of emission of photons if the frequency is increased whilst keeping intensity constant?

• Solution: 𝐼 = 𝑃

𝐴=

𝐸 𝑝𝑒𝑟 𝑝ℎ𝑜𝑡𝑜𝑛 ×𝑝ℎ𝑜𝑡𝑜𝑛 𝑟𝑎𝑡𝑒

𝐴

• 𝐸∞𝑓, A = constant, I = constant, but E ↑

• This means photon rate must decrease

• Increasing frequency whilst keeping intensity constant decreases rate of emission of photons

• There is no delay between incident light ray and ejected photoelectron

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These observations cannot be explained with the wave theory • A wave of any energy should eventually bring

enough energy to the metal plate

• Einstein explained the observation:

Light arrives in photons

This photon must have the right frequency to give the electron the necessary escape energy

1 photon gives all its energy to 1 electron

1 electron can only accept 1 photon of energy Brighter light more e’s are emitted

Frequency: energy of photon KE of photoelectron

𝑓∞1

λ, λ ↑ 𝑚𝑒𝑎𝑛𝑠 𝑓 ↓ and vice versa

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Explaining observation from Gold leaf experiment

• Zinc sheet has a certain work function work function is the energy needed to do the work to overcome the attractive forces that act on the electron within the metal

• Photons must have energy greater than this to be able to eject electrons

• UV radiation has the highest energy

A) very intense visible or infra red light incident

• leaf remains diverged

• intensity only increases number of photons incident per second

• long λ and low f

• none of the photons has enough energy to liberate electrons

• leaf stays diverged

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…continued B) low intensity UV light • leaf falls immediately • 1 photon reacts with 1 electron • no time needed to build up energy C) placing a sheet of glass between the UV source and zinc • leaf does stay diverged • Glass only transmits low energy visible light • High energy UV photons are absorbed D) zinc sheet charged positively • leaf remains diverged for all λ • Raising the potential of the metal causes a

much deeper potential well to escape from • Photons no longer have sufficient energy to liberate

electrons • This is similar to replacing zinc with a metal that has a

greater work function • This is like being trapped in a well with vertical walls and

trying to jump out in one leap

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Experimental procedure • Illuminating one of two metal plates in an evacuated tube,

where a potential difference of about 10V has been applied between anode and cathode, will cause electrons to be emitted from the cathode

• They are accelerated across the vacuum by the PD

• This creates a small current, which can be measured by a galvanometer

• No UV light incident, no current flows

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Results • Each metal has a certain frequency 𝑓0 of light below which no

e’s are ejected

• I and II are different metals

• Above 𝑓0 the greater the intensity, the higher the current

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Reversing the potential • Impose an opposing potential

(the retarding potential) between the two metal plates

• This makes the anode negative • The kinetic energy of the

photoelectrons can be reduced to zero the electron current is stopped.

• By observing the value of the retarding or stopping potential, 𝑉𝑆, the kinetic energy of the photoelectrons can be calculated from the electron charge e, its mass m and the frequency of the incident light

• 𝑉𝑠𝑒 =1

2𝑚𝑒𝑣𝑚𝑎𝑥

2

PD = 𝑒𝑛𝑒𝑟𝑔𝑦

𝑐ℎ𝑎𝑟𝑔𝑒

𝑒𝑛𝑒𝑟𝑔𝑦 = 𝑃𝐷 × 𝑐𝑕𝑎𝑟𝑔𝑒 = 𝑉𝑠𝑒

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• Increasing the retarding potential to the anode results in a decrease in current, no matter how intense the light is

• This suggest the photoelectrons are emitted with the same KE regardless of intensity of incident light

• Same wavelength light all have same stopping potential

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Stopping potential

• Different frequencies of light directed at the same metal surface have different stopping potentials

• The greater the frequency of incident light, the greater the stopping potential

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EXAMPLE: Complete the table…

The photoelectric effect

The photoelectric effect and classical wave theory compared…

Characteristics observed in the photoelectric

effect.

Classical Wave

Theory OK?

Ip is proportional to the light’s intensity.

Ip is zero for low enough cutoff frequency f0

regardless of the intensity of the light.

Ip is observed immediately even with a low

intensity of light above the cutoff frequency f0.

EK is independent of intensity of light.

EK is dependent on frequency of light.

Check your knowledge

Summary Observation

• Emission of e’s instantaneously without intensity of incident radiation influencing it

• The existence of a threshold frequency

Classical theory

• Energy should be absorbed continuously if light is a wave, until e’s have enough energy to break free

• Less intensity should mean less energy incident, therefore the longer it should take for the e’s to be ejected

• Intensity of radiation is independent of frequency

• Emission of e’s should occur for all frequencies

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Summary of experimental results

• Current is linearly proportional to intensity

• Current appears without delay

• e’s are only emitted if f > 𝑓0 ( same as if λ is short enough, f = 1

λ)

• Maximum KE of photoelectrons increases linearly with f 𝐾𝐸𝑚𝑎𝑥 = −𝑉𝑆

• 𝑓0 depends only on type of metal

• Increasing intensity increases the number of ejected photoelectrons, but each electron carries the same average energy (frequency did not change)

• Increasing frequency whilst keeping intensity constant decreases the rate of emissions of photoelectrons

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