Fun with Kinetic Energy

[bgiorgi_3A]

Hey chem friends! I am completely lost on this problem and I was wondering if I could get some help setting it up? Thank youuuu!

Q7. A particular metal is illuminated by UV photons of wavelength 210 nm and electrons of energy up to 1.25 eV are emitted from the surface. What is the maximum kinetic energy of the photoelectrons emitted when the UV photons are, instead, 175 nm in wavelength?

[Wasila Sun 2I]

Given that the metals in both instances are the same, I know that the work of both instances will be equal. The equation for work is work=E(photon)-E(kinetic). The equation for energy of a photon can be expressed as E=ch/wavelength by combining E=hv and c=v*wavelength, and the kinetic energy is given. So to set up the problem, I would do (ch/wavelength1)-E(kinetic1)=(ch/wavelength2)-E(kinetic2). Then you can plug in the constants c and h, the given wavelengths, and the given first kinetic energy. Solve for the 2nd kinetic energy. I think the answer should be 2.44 eV.

[AnnaNovoselov1G]

Hello!

1. Consider the equation E (kinetic) = E (photon) - work function. E (photon) is h x frequency.
You know that the kinetic energy of the electrons would be 1.25 eV. Convert that to Joules by using the relationship 1eV=1.62 x 10^-19 Joules. You can also find the energy of the photon since you know the wavelength. Use the relationship c=frequency x wavelength to find frequency (remember to convert nm to m). Then, calculate the E(photon) using E= h x frequency.
2. Now that you know E (photon) and E (kinetic), you can calculate the work function for the metal.
3. Now, convert 175 nm to frequency and then calculate the E (photon) generated by that wavelength. From there, you can calculate the kinetic energy.

Hope this helps!