Threshold frequency and ejection of electrons

Oct 2016
3
0
A sample of silver having a threshold frequency of 1.09 x 10 15 Hz is exposed to an ultraviolet light source (λ= 200 nm). This results in the ejection of electrons. What changes will be observed if:

The silver is replaced with aluminum (threshold energy = 9.82 x 10 14 Hz)
a) No electrons are ejected
b) More electrons are ejected
c) Slower electrons (on average) are ejected
d) Fewer electrons are ejected
e) Faster electrons (on average) are ejected

Half of the ultraviolet light from the source is blocked:
a) No electrons are ejected
b) More electrons are ejected
c) Slower electrons (on average) are ejected
d) Fewer electrons are ejected
e) Faster electrons (on average) are ejected

The ultraviolet source is replaced with a red laser that emits the same number of photons per unit time as the original ultraviolet source:
a) No electrons are ejected
b) More electrons are ejected
c) Slower electrons (on average) are ejected
d) Fewer electrons are ejected
e) Faster electrons (on average) are ejected

An ejected electron has velocity of 5.0 × 104 m/s. What is the de Broglie wavelength of this electron?
 
Jun 2016
24
3
What have you come up with so far for this problem? Any guesses or attempts?

To get you started, you should check your course material on the photoelectric effect and the ultraviolet catastrophe. You'll see that electrons won't be liberated from atoms unless the individual photon energy (frequency, for your problem here) exceeds some threshold, specific to the material in question (silver or aluminum in your problem). If the photons lack the minimum energy (frequency) necessary, then cranking up the intensity of that light (bombarding with more photons per second) at the same frequency, will do nothing. But having extra individual energy in the photons (frequency higher than the threshold) will result in extra kinetic energy for the liberated electrons, correlating to the answer "faster electrons are ejected".

For the first step in your problem, we see that electrons are ejected from sliver by UV light at a certain wavelength (corresponding to a certain frequency), so we know we've matched or exceeded the threshold. Now look at aluminum's threshold. How does it compare to silver's? We're using the same photons as before. Would you conclude that the photon's energy falls short of the threshold (no electrons ejected), or exceeds by even more than with silver (faster electrons ejected)?

Now see what you can do with the other sections of the problem.
 
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