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Hello, I know that the notion that short wavelengths can eject e-, while long wavelengths cannot. However, I am unsure of the reasoning behind this and how this idea came about, so I would greatly appreciate it if someone helped explain this to me.
All metals have a specific work function or threshold, which is the minimum energy required to eject an electron. Shorter wavelengths usually have an energy greater than the threshold whereas longer wavelengths do not, which is why light with shorter wavelengths are more commonly able to eject electrons. When the photons of the shorter wavelength interact with the electrons of the metal, the photon's energy is transferred and the electron then has enough energy to be ejected. I'm not sure if I answered your question, but I hope this helps.
Short wavelengths can eject the electron because as Johnathan said they have a higher energy. The energy equation is E = hv. H is planck's constant, so that value never changes. However, the v is in regards to frequency, and we know that wavelength and frequency are inversely proportional (c = λ * v). So, a shorter wavelength results in a higher frequency resulting in higher energy, which is the reason that they are able to eject the electrons from the metal's surface.
Longer wavelengths have less energy than shorter wavelengths due the energy = hc/wavelength formula that denotes that if the wavelength increases, then the energy of the particle will decrease which establishes a negative correlation. In conclusion, shorter wavelengths shoot out electrons compared to longer wavelengths that do not shoot out electrons because they do not have enough energy.
For an electron to be ejected from a metal, there is a threshold energy that each photon must meet. For every one photon that meets the threshold energy, one electron will be emitted from the metal. If the wavelength is longer than the threshold energy, then there would not be enough energy for each photon to eject an electron.
It's a general concept that as frequency increases, wavelength decreases. Frequency is inversely proportional to energy per photon. In the case of attempting to emit electrons from metal surfaces, you would need a specific frequency corresponding to energy. Rather than looking at the wavelength, its more relevant to consider the energy per photon at certain levels of frequency. :)
A photon must be able to reach the threshold energy required to eject an electron. Consider that the longer the wavelength, the lower the frequency, and the energy off each photon is proportional to its frequency, given by E=hv. Therefore, shorter the wavelength is, the more energy it has.
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