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**QUANTUM PHYSICS**

**The Photo-Electric Effect**

photons |

__History__

**Hertz** discovered the photo-electric effect in 1887.

His experiment concerned two parallel metal electrodes, with a p.d. across them. He observed that when ulta-violet light was shone on the electrodes an electric spark jumped between them.

Many of the properties of the effect were established by **Hallwachs** and **Lenard** in the years leading up to Einstein's theory in 1905.

__The Photon Model __

Max **Planck**(1901) first proposed the idea that light was emitted as discrete __packets of energy__ called **quanta**. He also showed that each packet (**quantum**) had energy given by the equation:

where,

**E **= energy (J)

**h **= Planck's constant, 6.626 x 10^{-34} Js

* ν*(nu) = frequency of light radiation (Hz, s

^{-1})

However,** Einstein**, as part of his photo-electric effect theory, described these quanta as streams of __particles__, which he termed **photons**.

__Observations__

1. Emission of photo-electrons only occurs if the frequency of incident radiation exceeds a minimum value called the **'threshold frequency**'.

2. The emission of photo-electrons starts __immediately__ the surface becomes irradiated(provided the frequency of the radiation is above the thresh-hold frequency).

3. If the incident radiation has a frequency above the thresh-hold frequency:

(** no. electrons emitted/sec.** ) (** radiation intensity** )

4. Increasing the __frequency__ of the incident radiation has the effect of increasing the __kinetic energy__ of **all** emitted electrons. Hence the maximum kinetic energy an electron may have is increased by increasing frequency.

5. Radiation __intensity__ is **independent** of __electron kinetic energy__. The kinetic energy of electrons is soley controlled by the radiation frequency.

__Wave Theory Predictions__

Classical wave theory predicts that energy is carried in the wave-front.

Electrons absorb the energy from the wave until the level __exceeds__ the **work function***.

Electrons are then released from the surface of the metal.

***W** (or *Phi* **Φ**) work function - minimum energy to remove an electron

__Three__ main predictions come from this classical explanation:

1. Radiation intensity is proportional to the resulting maximum electron kinetic energy.

(**radiation intensity**) (**maximum electron kinetic energy**)

2. The effect should occur for __any__ frequency of light.

3. There is a __delay__ between the radiation contact with the surface and the first release of electrons.

__Einstein's Photo-Electric Effect Theory__

The theory is based on a **beam of light **being considered as a **stream of photons**, each with energy **h ν**.

Before explaining the theory in more detail, it is important to appreciate what is meant by '**the intensity of light**'.

Consider photons emitted from a point source.

The sphere around the point, where the photons arrive, enlarges with distance from the point.

So at large distances the photons are spread out over a large area.

Note there is **no** diminuition of photon energy, whatever the distance travelled.

**Intensity (I) beam of light (no.photons/m ^{2}/sec.) **

**Einsein's big idea**: In essence, this was that when a photon collides with an electron, there are two possible outcomes:

1. The photon __reflects__ from the electron with **no energy transfer**.

2. The photon is __absorbed__ by the electron and gives up **ALL** its energy to it.

Photons are paired with electrons. So there is no question of one photon sharing energy with more than one electron.

**intensity of light ( no. electrons emitted by a surface)**

or more accurately,

**(no.photons/m ^{2}/sec.) ( no. electrons/m^{2}/sec.)**

So when a photon arrives at the surface, an electron is emitted. This explains the instantaneous nature of the phenomenon.

The photon energy received is used to overcome the forces holding the electron within the surface and to give it kinetic energy to escape.

Einstein's photo-electric effect equation describes this process in more detail:

Note this involves the __maximum__ electron kinetic energy. Many electrons emerge from the surface with **less **than the maximum energy. This is a result of energy lost in collisions before they are free.

**W **is called the '**work function**' of the surface.

It is a measure of the energy that binds each electron into the surface. The constant is different for different materials.

That there must be a minimum frequency for electron emission is implicit.

If,

there is not enough energy available to release an electron.

However, that __particular__ frequency for an electron to be released is given by:

where ** ν_{o}** is the threshold frequency.

Using **c = ν _{o}λ_{o}** and substituting for

*=*

**ν**_{o}**c/λ**, the threshold wavelength

_{o}**λ**is given by:

_{o}

__Millikan's Apparatus__ - **stopping potential**

In **1916** **Millikan** devised a series of experiments that completely vindicated Einstein's theory.

Using **monochromatic** **light**, the apparatus tested three surfaces in turn (**lithium**, **sodium** and **potassium**).

He found that **altering the potential **between the surface and the electron collector electrode, altered the '**electron current**'.

When a **small positive potential** was applied to the metal, only electrons with enough KE escaped to impact on the collector electrode.

The remainder were pulled back to the surface. So only a small electric current was detected at the electrode.

With **increased positive potential**, the electron **current was reduced**.

Eventually there came a point when the current reduced to zero. This corresponded to electrons with the maximum KE being stopped from reaching the collector.

This p.d. between both electrodes is called the **stopping potential** **V** .

We can now integrate 'stopping potential' into the photo-electric effect equation.

The work done by an electron in moving against the 'stopping potential'(ie against the 'electric field' ) is equal to the maximum KE of the electron.

from Einstein's photo-electric effect equation:

substuting for KE,

rearranging into the form for a straight line ' **y = mx + c** '

For different materials, a plot of **V** against frequency * ν*(nu) is a straight line, with intercepts on the

**V**-axis and the

*-axis.*

**ν**

intercept on** V**-axis ( ν = 0 ) is:

intercept on the * ν*-axis (V = 0 ) is:

where * ν_{o}* is the threshold frequency

The gradient is given by :

__notes__

1. For different materials the graph has the same gradient, but different intercepts.

2. From the graph, measurements of **W** (the work function) and **h** (Planck's constant) can be made.

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