What Are the Effects of Light Wavelength on Photoelectron Production?

[kevnm67]

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!

 

[da_nang]

I can see why some of the answers differs from the correct ones. In b), since you like to use rounded values for your calculations, I assume you used 3*10⁸ m/s for the speed of light in vacuum? Dividing this with the given answer from a will make your answer deviate. It all comes down to the accuracy of the values you used in your calculations. [3*10⁸]/[7*10¹⁴] m deviates by 0.13 % whereas [2.998*10⁸]/[7*10¹⁴] m deviates by 0.07 %, [2.99792458*10⁸]/[7*10¹⁴] m by 0.06 %. Of course, it also depends on what level of accuracy the makers of the question used as [4.135669*10^-15*2.99792458*10⁸]/[2.9] m deviates by 0.11 % but is lucky enough to be rounded to the correct value.

In c it's basically the same thing - accuracy. Although, here there's also the number of significant figures to consider. You've rounded to one significant figure, which would be correct to do since the given information for the calculations gives the least number of significant figures as one. So based on that, I would say 3 nm is allowed. However, since you're given multiple answers to choose from, you'd be better of by choosing the one that comes the closest to the answer in the calculations.