Radiation with a wavelength of 238 nm shines on a metal surface and ejects elect
ID: 1491153 • Letter: R
Question
Radiation with a wavelength of 238 nm shines on a metal surface and ejects electrons that have a maximum speed of 3.75times10^5 m/s. 1) Which of the following metals is it? (The values in parentheses are the work functions) potassium (2.24 eV) calcium (2.71 eV) gold (4.82 eV) uranium (3.63 eV) 2) What minimum frequency of light is need to eject any electrons? 1.16times10^15 Hz 1.26times10^15 Hz 1.36times10^15 Hz 1.46times10^15 Hz 1.56times10^15 Hz 3) What is the momentum of a single photon with the frequency you just determined above? 1.57times10^-27 J-s/m 2.57times10^-27 J-s/m 3.57times10^-27 J-s/m 4.57times10^-27 J-s/m 5.57times10^-27 J-s/mExplanation / Answer
1) gold(4.82 eV)
given
lamda = 238 nm
vmax = 3.75*10^5 m/s
use Einstein's equation
E_photon = Wo + KE_max
==> Wo = E_photn - KE_max
= h*c/lamda - 0.5*m*v^2
= 6.626*10^-34*3*10^8/(238*10^-9) - 0.5*9.1*10^-31*(3.75*10^5)^2
= 7.71*10^-19 J
= 7.71*10^-19/(1.6*10^-19) eV
= 4.82 eV
2) 1.16*10^15 hz
f = Wo/h
= 7.71*10^-19/(6.626*10^-34)
= 1.16*10^15 hz
3) 2.57*10^-27 J-s/m
Apply, P = E/c
= h*f/c
= 6.626*10^-34*1.16*10^15/(3*10^8)
= 2.57*10^-27 J-s/m
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