The following table lists the work functions of a few common metals, measured in

Question

The following table lists the work functions of a few common metals, measured in electron volts. Using these data, answer the following questions about the photoelectric effect. Part A Light with a wavelength of 190 nm is incident on a metal surface. The most energetic electrons emitted from the surface are measured to have 4.0 eV of kinetic energy. Which of the metals in the table is the surface most likely to be made of? Part C Light with some unknown wavelength is incident on a piece of copper. The most energetic electrons emitted from the copper have 2.7 eV of kinetic energy. If the copper is replaced with a piece of sodium, what will be the maximum possible kinetic energy K of the electrons emitted from this new surface?

Explanation / Answer

ANSWER

Part A

Keep in mind that there are a couple of equations that we need to solve this problem. The first is,

E=hf (photon energy is equal to Plank's constant times the frequency)

The second equation to keep in mind here is,

K(max)=hf- (or rather, the maximum kinetic energy is equal to the photon energy minus the work function)

In part A, we are solving for the work function and we can re-write the equation as:

hf-K(max)=

We know that K is equal to 4 eV (remember that 1 eV=1.6x10-19 J)

But what about hf?

We know that E=hf, yet f is equivalent to c/ (the speed oflight divided by the wavelength)

Plugging this in we get,

hc/-K(max)=

(6.626x10-34J)(3x108)/(1.9x10-7m)-(4eV)(1.6x10-19J)= 2.53 eV,

indicating that the surface is most likely made out of lithium.

Part B

Here we are looking for the photon energy, thus we use the equation,

E=hf, or as we saw in Part A, E=hc/

Plugging it in we get:

E=(6.626x10-19J)(3x108)/(5.1x10-7m)
E=3.89x10-19J

Dividing this by 1.6x10-19 J we get the answer as 2.43eV. There are three possible metals that could be ejected here; cesium, potassium, and sodium.

Part C

We start by finding the wavelength of light using the given information for copper.

=(hc)/(K+)
=(hc)/(2.7eV+4.5eV)
=(hc)/(1.152x10-18J)
=173nm

We then use this to find the maximum kinetic energy with sodium:

K=hc/173-
K=hc/173-2.3eV
K=4.9eV

Regards!!!

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