photoelectric effect

[stickplot]

1. The problem statement, all variables and given/known data

a. Does the photoelectric effect take place if mercury is illuminated with UV light with a wavelength λ = 300 nm? The cutoff wavelength for mercury is 250 nm.

b. What is the maximum kinetic energy of the electrons liberated by this radiation from lithium (W = 2.3 eV) and beryllium (W = 3.9 eV)?

2. Relevant equations

hc/w

3. The attempt at a solution

a. longer wavelength = lower frequency = lower energy, So no photoelectric effect

b. (6.63x10^-34)(3x10^8)/(300x10^9)(1.6x10^-19)= .04 eV
lithium Kmax= 2.3-.04=2.26 eV
beryllium Kmax=3.9-.04=3.86 eV

im pretty sure about my a answer but the b is the one that im having trouble with anyone see any problems with how i did b?

[buffordboy23]

Your answer to part a) shows that you understand the conceptual aspects of the photoelectric effect.

However, your answer to part b) is wrong. Part b) wants to you to find the maximum kinetic energy. Does your given equation have units for energy? No. Check it. When in doubt, always check your units.

EDIT: See link for more info:
http://en.wikipedia.org/wiki/Photoelectric_effect#Equations

EDIT 2: Forget my previous response to part b) about the units. Your use of "w" for two different quantities confused me. I now see that "w" can also stand for the wavelength.
You should know that your answer to part b) is wrong based on your answer to part a). According to what I see, you inputted the wrong wavelength; you have it to a positive power, when it should be to a negative power.

[stickplot]

o ok i see what i did wrong i multiplied the nanometers by ^positive 9 instead of negative. how does that look?
(6.63x10^-34)(3x10^8)/(300x10^-9)(1.6x10^-19)= .04 eV
lithium Kmax= 2.3-4.125=-1.825 eV
beryllium Kmax=3.9-4.125=-.225 eV

[buffordboy23]

Good. Your answers look like they have the right magnitude, but kinetic energy always has a positive value.

The equation that describes the photoelectric effect is given by

K_max = hf - W

where K_max is the maximum kinetic energy of the escaped electron, h is planck's constant, f is the frequency of the photon, and W is the required energy to knock an electron loose from a particular atom.

Important conclusion: If hf < W, which implies that K_max < 0, the electron cannot be knocked free.

[stickplot]

o ok i see what i did wrong. how does that look?
lithium Kmax= 4.125-2.3= 1.825 eV
beryllium Kmax=4.125-3.9= .225 eV

[buffordboy23]

It looks good...I didn't check the numerical accuracy (you can do that), but the magnitudes look right.