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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/m

Explanation / 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