Radiation with a wavelength of 238 nm shines on a metal surface and ejects elect
ID: 1457974 • Letter: R
Question
Radiation with a wavelength of 238 nm shines on a metal surface and ejects electrons that have a maximum speed of 3.75x10^5 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? 1.16x10^15Hz 1.26x10^15Hz 1.36x10^15Hz 1.46x10^15Hz 1.56x10^15Hz 3) What is the momentum of a single photon with the frequency you just determined above? 4) If radiation with wavelength of 150 nm is used, what will the maximum speed of the ejected electrons be? 5) How fast must an electron (m = 9.11x10^-31 kg) be moving to have a DeBroglie wavelength of .282 nm? 6) How fast must a neutron (m = 1.67x10^-27 kg) be moving to have a DeBroglie wavelength of .282 nm? 7) How fast must a ball (m = .46 kg) be moving to have a DeBroglie wavelength of .282 nm?Explanation / Answer
1)
= c/f
f = c/
f = 300*10^6/(238*10^-9) = 1.26*10^15 hz
Let's consider Einstein's equation for the photoelectric effect:
(1/2)mv^2 = hf - W
where:
m is the electron mass 9.11*10^-31 kg
v is the maximum speed of the elecrons ejected
h is the Plank constant 6.63*10^-34 Js
f is the frequence of the shining radiation
W is the metal work function
W = hf - (1/2)mv^2 = 6.63*10^-34*1.26*10^15 - (1/2)*9.11*10^-31*3.75^2*10^10 =
W = 8.35*10^-19 - 64*10^-21 = 7.71*10^-19 J
1 eV = 1.6*10^-19 J
W = 7.71/1.6 = 4.82 eV
The metal is gold.
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