synchrotron multiple choice question, help

[tha boss]

Scott is working in the new synchrotron and is currently bombarding a material of work function 3.2eV with X-rays of wavelength 0.3nm. an electron is ejected from the material with kinetic energy 27eV.
The wavelength of the scattered photon is closest to:
a) 3.5nm
b) 0.3nm
c) 0.5nm
d) 3.2nm

[Shark 774]

Initial energy of photon = hc/wavelength = 6.63 x 10^-16J
Work function in joules = 5.12 x 10^-19
Kinetic energy of electron in joules = 4.32 x 10^-18

Initial energy of photon = final energy of photon + kinetic energy of electron + energy needed to remove electron (i.e. work function)

Therefore the energy of the scattered photon = the intial photon energy - the kinetic energy of the electron - the energy needed to remove the electron

i.e. E (scattered photon) = 6.63 x 10^-16    -    5.12 x 10^-19    -    4.32 x 10^-18   = 6.58 x 10^-16J
Wavelength of scattered photon = hc/E = 3.022 x 10^-10 = 0.3022 x 10^-9 which is closest to answer B, although of course answer B is rounded, because if it were exactly 0.3 then there would be no change in wavelength and that isn't possible here. Hope this helps.

[thatricksta]

Initial energy of photon = hc/wavelength = 6.63 x 10^-16J
Work function in joules = 5.12 x 10^-19
Kinetic energy of electron in joules = 4.32 x 10^-18

Initial energy of photon = final energy of photon + kinetic energy of electron + energy needed to remove electron (i.e. work function)

Therefore the energy of the scattered photon = the intial photon energy - the kinetic energy of the electron - the energy needed to remove the electron

i.e. E (scattered photon) = 6.63 x 10^-16    -    5.12 x 10^-19    -    4.32 x 10^-18   = 6.58 x 10^-16J
Wavelength of scattered photon = hc/E = 3.022 x 10^-10 = 0.3022 x 10^-9 which is closest to answer B, although of course answer B is rounded, because if it were exactly 0.3 then there would be no change in wavelength and that isn't possible here. Hope this helps.

This is great, but I must ask - Why do you bother converting to Joules? I think you would have saved time working in eV since plancks constant in eV is 4.14*10-14

[Shark 774]

Initial energy of photon = hc/wavelength = 6.63 x 10^-16J
Work function in joules = 5.12 x 10^-19
Kinetic energy of electron in joules = 4.32 x 10^-18

Initial energy of photon = final energy of photon + kinetic energy of electron + energy needed to remove electron (i.e. work function)

Therefore the energy of the scattered photon = the intial photon energy - the kinetic energy of the electron - the energy needed to remove the electron

i.e. E (scattered photon) = 6.63 x 10^-16    -    5.12 x 10^-19    -    4.32 x 10^-18   = 6.58 x 10^-16J
Wavelength of scattered photon = hc/E = 3.022 x 10^-10 = 0.3022 x 10^-9 which is closest to answer B, although of course answer B is rounded, because if it were exactly 0.3 then there would be no change in wavelength and that isn't possible here. Hope this helps.

This is great, but I must ask - Why do you bother converting to Joules? I think you would have saved time working in eV since plancks constant in eV is 4.14*10-14

Good point! I didn't know the value for planck's constant in terms of eV, but that's a thing I should learn!

[Lasercookie]

Good point! I didn't know the value for planck's constant in terms of eV, but that's a thing I should learn!

Don't worry, it is on the formula sheet.

thatricksta made a small typo, it's not ^-14