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fluidistic
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Homework Statement
Photons with wavelength of 450 nm hit a metal. The trajectory of the most energetic electrons detached from the metal follow a circular path of radius 0.2 m due to a magnetic field of magnitude [itex]2 \times 10 ^{-5}T[/itex]. What is the work function of the metal?
Homework Equations
Lorentz's force. Kinetic energy of electrons: [itex]\gamma m_e v^2[/itex].
Centripetal force: [itex]F_c = \frac{m_e v^2}{r}[/itex].
Conservation of energy.
The Attempt at a Solution
The energy of a photon hitting the metal is equal to the work function of the metal plus the kinetic energy of a most energetic electron.
[itex]E=hc/lambda \approx 4.42 \times 10 ^{-19}J=2.76 eV[/itex].
I reach, using the mentioned equations (and using the fact that the centripetal force is worth the Lorentz force, that is [itex]F_c=e^- vB[/itex]) that v of the most energetic electrons is worth [itex]v=\frac{e^- Br}{m_e}[/itex]. It seems that the gamma factor for my calculator is worth 1 so basically the speed of the most energetic electrons aren't big at all compared to c.
This gives me a kinetic energy of approximately [itex]4.51 \times 10^{-19}J[/itex] or 2.81 eV; which is greater than the energy of any photon, which is totally impossible.
For the arithmetics/algebra, I used as many digits as I could.
[itex]m_ e=9.10938215 \times 10 ^{-31}kg[/itex].
[itex]e^- =1.602176487 \times 10 ^{-19}C[/itex]. However I took c as 3x10^8 m rather than the exact value, but this won't change anything anyhow.
[itex]h=6.62606896 \times 10^{-34}J[/itex].
What am I doing wrong?Edit: I just see that I forgot to divide by 2 the kinetic energy... I don't think it should change a lot, but still, I'll redo the math.
Edit 2: I get that the work function is worth approximately [itex]1.350055399 eV[/itex] which seems in theory possible. However when I look in tables on the Internet, I see no metal even close to this. The smallest work functions I see are over 2 eV.
Can someone confirm/infirm my answer? Thank you.
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