- #1
kevnm67
- 43
- 0
Homework Statement
A photocathode whose work function is 2.9 eV is illuminated with white light that has a continuous wavelength band from 400 nm to 700 nm.
A) What is the threshold frequency for photoelectron production?
a. 4 x 1014 Hz b. 7 x 1014 Hz c. 13 x 1014 Hz
B) What is the range of the wavelength band (in nm) in this white light illumination for which photoelectrons are produced?
a. 428 nm to 700 nm b. 400 nm to 428nm c. 300 nm to 400 nm
C) What is the deBroglie wavelength of an emitted electron with kinetic energy of 0.2 eV?
a. 2.5 nm b. 1.2 nm c. 2.7 nm
Homework Equations
f0 = E0/h
l = h/mv
c= f l
The Attempt at a Solution
I want to make sure I am solving these questions correctly. Here is what I did:
a) f0 = 2.9eV/4.14x10-15 = 7 x 1014
b) c = f l
=429 nm
So I said the range would start at 400 and go up to 429nm...the answer was 400-428 nm
c) l = h/mv
m= 9.11 x 10-31
v= 2.65 x 105 which I got from using 1/2 mv2=.2eV
I multiplied .2 eV by 1.6 x 10-19 J to get K
then squrt (2 x K/mass of electron)
l = (6.63 x 10-34J s)/(9.11 x 10-31)(2.65 x 105 m/s) = 3 nm
The answer was 2.7 nm
I wasn't sure if I was rounding differently or maybe did something wrong? Thanks for the help!