1.2 The Photoelectric Effect

Photoelectric effect refers to the phenomenon of light producing a flow of electricity upon a metal surface.

The effect was first demonstrated by Heinrich Hertz in 1880s. It is not well-explained until Albert Einstein proposed an explanation in 1905.

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1.2.1 Terminologies and Main Results

• Work function \(\phi\): the minimum energy required to free an electron.

• Stopping potential: the potential difference that just enough to stops electrons.

• Threshold wavelength: the maximum wavelength for which electrons are freed. Corresponding minimum frequency is the threshold frequency.

• New energy unit - electronvolt: an electronvolt (\(eV\)) is the amount of kinetic energy gained by a single electron accelerating through an electric potential difference of one volt in vacuum. Conversion: $$1eV=1.602\times10^{-19}J.$$

Energy of a photon is$$\bbox[silver]{E=hf}.$$ Each photon with sufficient energy is able to help one electron overcome the work function and bring it out of metal surface. To conserve the energy, the maximum possible kinetic energy of an electron is $$\bbox[silver]{K.E._{\text{max}}=hf-\phi}.$$

1.2.2 The Production of X-Rays

• Bremsstrahlung: "braking radiation".

• Cutoff wavelength: minimum wavelength possible.

When producing X-rays, electrons are accelerated, smashed onto a target, and rapidly slow down. As it undergo a large acceleration, powerful electromagnetic waves are created. Since electromagnetic waves can be quantized, maximum energy (similarly maximum frequency or minimum wavelength) of produced X-rays can be calculated based on the maximum kinetic energy of electrons (See problem 4 for detail).

Problems

1. As a review for 1.1, What is the peak wavelength for black body radiation due to human body?

   (Hint: Using Wein's law)

2. (Harris) Light of 300 nm wavelength strikes a metal plate, and photoelectrons are produced with speed of 0.002c.

   (a) What is the work function of the metal?

   (b) What is the threshold wavelength then?

3. (Harris) A 940 kHz radio station broadcasts 40 kW power. How many photon are transmitted per second?

4. (Harris) A television picture tube accelerates electrons through a potential difference of 30,000 V. Find the cut-off wavelength fo X-ray produced.

   (There are protection mechanism shielding the X-ray. Also this type of televisions are not that common nowadays.)