Sapling HW (Max Wavelength of Radiation)

[Kainalu Puu-Robinson]

As you may well know, placing metal objects inside a microwave oven can generate sparks. Two of your friends are arguing over the cause of the sparking, with one stating that the microwaves "herd" electrons into "pointy" areas of the metal object, from which the electrons jump from one part of the object to another. The other friend says that the sparks are caused by the photoelectric effect. Prove or disprove the latter idea using basic physics.

Suppose the typical work function of the metal is roughly 3.600×10−19 J. Calculate the maximum wavelength in angstroms of the radiation that will eject electrons from the metal.

I'm having trouble with this problem, could someone walk me through how they did it?

[Jeffrey Doeve 2I]

So, in order to eject electrons, the energy of a photon must equal or be greater than the work function. Based on the statement the maximum wavelength(or minimum frequency), we can set energy of a photon(hc/wavelength) equal to work function and solve for wavelength. The wavelength answer we get would be in meters, so we divide by 1*10^-10 to get the answer in Angstroms. Hope this helps!

[Joseph Hsing 2C]

Since you are finding the wavelength of the threshold energy needed to eject electrons, then you can disregard kinetic energy.

Set work function equal to h*frequency to find frequency.

Next, use c=lambda*frequency to solve for wavelength.

Hope this helps :)

[Elena Chen 2E]

Since the work function is given and they are asking for the wavelength, use the equation E=(hc)/lambda to convert energy to wavelength. Then convert the wavelength units from meters (SI unit) to angstroms, which is given on the constants and equations sheet.

I believe they give you the radiation in GHz (at least, that was my question) of the microwave oven, so just convert that number to either energy (in J) or wavelength (in meters or angstroms) so you can compare it with the work function. If the energy matches or is greater than the work function, then the photoelectric effect is possible.

[Hannah Alltucker 3L]

For starters, you need to know workfunction=Energy - KEnergy, which is also written as hv-.5mv^2. To find the minimum energy needed, there is no extra kinetic energy being released, so kE is zero.

This will give us workfunction=hv-0, which you can manipulate to find v (frequency). Angstroms are measured in 10^10, so make sure you multiply your final value.

For the second question we know wavelength x v=c. Manipulate this to solve for wavelength and compare your calculated value to your first answer. This way you can determine if there is enough energy to eject electrons.

[Kainalu Puu-Robinson]

So, in order to eject electrons, the energy of a photon must equal or be greater than the work function. Based on the statement the maximum wavelength(or minimum frequency), we can set energy of a photon(hc/wavelength) equal to work function and solve for wavelength. The wavelength answer we get would be in meters, so we divide by 1*10^-10 to get the answer in Angstroms. Hope this helps!

Oh yes, I was forgetting the very last step so my decimal place was off. Thanks for the help!

[Kiana Rogers 1E]

For the second part of the problem, if the wavelength is greater than the maximum wavelength, the microwave cannot eject electrons from the metal, therefore the photoelectric effect would not be the cause of the sparks.