Planck's Constant measured in photoelectric effect

[jimmypoopins]

Homework Statement

In an advanced laboratory class a student performs the photoelectric experiment. Ultraviolet light is shone on a particular metal and the stopping potential is measured at the same time. It is found that 2.61 V is needed to stop all the electrons when the wavelength of the light is 285 nm, and 4.53 V for a wavelength of 207 nm. What is the work function of the metal?

Homework Equations

$$hf=eV+\phi$$
Find $$\phi$$

The Attempt at a Solution

(1)$$hf_{1}=eV_{1}+\phi$$

(2)$$hf_{2}=eV_{2}+\phi$$

divide 1 by 2 to get rid of h, and we get

$$\frac{f_{1}}{f_{2}}=\frac{eV_{1}+\phi}{eV_{2}+\phi}$$

i can't seem to solve for $$\phi$$ and get the correct answer. I've tried doing it both algebraically(sp, sry) and with a calculator. possibly I'm putting the numbers in wrong? i have:

$$e=1.6022*10^-19 C$$

$$f_{1}=285*10^-9 m$$

$$f_{2}=207*10^-9 m$$

$$V_{1}=2.61V$$

$$V_{2}=4.53V$$

where am i going wrong? please help

 

[JeffKoch]

Should you need two wavelengths to measure the work function in this experiment?

 

[jimmypoopins]

my apologies, i should have added something not stated in the problem. the second part of this problem is stated:

2. What is Planck's constant based on this measurement?

from this i assume that h is an unknown for part 1. my reasoning is that this is an experiment, and Planck's constant is not exact; it is just supposed to be calculated from four measurements someone took in a lab.