Conceptual Physics

(Sean Pound) #1

bullet will hit a bottle with more energy. The same number of bottles will still be hit; they
just go flying off the target faster.


In quantum theory, more “intensity” does not mean switching to a larger caliber, more
powerful rifle. More intensity means firing more bullets per second from the same rifle,
which means more bottles get knocked over. The increased intensity does not involve
changing the energy of the bullets, so the bottles always get struck with the same
amount of energy.


Quantum theory also explains why low-frequency light cannot cause any electrons at all
to be emitted. The energy of each photon equals hf. Using intense light of low
frequency means that many low-energy packets of light are striking the metal, but no
individual packet has enough energy to raise an electron to an energy level high
enough for it to escape.


The minimum energy an electron needs to escape the metal is called the work function,
and low-frequency photons have less energy than this. To use the rifle analogy:
Employing low-frequency light is like changing from bullets to spitballs. No spitball alone
has enough energy to knock over a target. In quantum theory, increasing the intensity of
light means the number of spitballs increases, not the energy of a spitball. Just as no
spitball is energetic enough to knock over a bottle, no low-frequency photon in the
experimental apparatus is energetic enough to free an electron.


Quantum theory (and Einstein) to


the rescue


More intense light ĺ more photons
More photons ĺ more ejected electrons

Frequency/energy of light and


electrons


Lower frequency light ĺ photons less
energetic
Less energetic photons cannot free
electrons

36.6 - Sample problem: photoelectric effect


The electrons in a particular metal have a range of different energies and require various amounts of additional energy in order to be “freed”
when the metal is struck by a photon.


The work function of a material is the least amount of energy required to release any electron from it. In other words, it is the amount of energy
required to free the “least attached” electron.


Variables


What is the strategy?



  1. Use the conservation of energy. This means that the energy of the incoming photon must equal the energy required to free the electron
    plus the kinetic energy of the electron as it flies away from the surface. (Ultraviolet light does have enough energy to free an electron in


Ultraviolet light with a frequency of


1.03×10^15 Hz is incident on a metallic


sodium surface. The work function,


the minimum amount of energy


required for an electron to be ejected


from this material, is ij = 2.36 eV.


What is the maximum kinetic energy


an escaping electron can have?


energy of photon E


maximum kinetic energy of electron KEmax


work function for sodium ij = 2.36 eV


Planck’s constant h= 6.63×10í (^34) J·s
frequency of ultraviolet light f =1.03×10 (^15) Hz


Copyright 2007 Kinetic Books Co. Chapter 36^667

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