Calculating Planck Constant and Work Function in Photoelectric Experiment

[georgeh]

In a photoelecric experiment in which a sodium surface is used, you find a stopping potential of 1.85V for a wavelength of 300nm, and a stopping potential of 0.820V for a wavelength of 400nm. From these data find (a) a value for the Planck constant, (b) the work function for sodium, and (c) the cutoff wavelength for sodium.
I tried solving (a) by stating the following
E=nh*f
h=E/f
h=E/(c/Lambda)
h=e*lamba/c ( i let n = 1)
And we know that K_max=e*delta V, where e is the Elementary charge, and DeltaV is the stopping potential.
I assumed that all the Energy is transffered to K_MAX
thus,
H=e*deltaV*lambda/C
The units end up working out, but the solution is wrong.
Anyone know what am i messing up on?
The rest of the question, i believe i can get once I solve this correctly

 

[Pengwuino]

Well you're assumption was incorrect. There is a certain energy called the work function that has to be overcome before an electron can be ejected.

$$E_{photon} = K + \phi$$

You can manipulate this equation to determine the equation for the kinetic energy of an ejected electron and it follows the form y=mx+b. The m will be your slope and it will actually be Planck's constant

 

[Gokul43201]

m will be the slope...when x represents the frequency and y represents the KE (stopping potential * e).

Alternatively, using the formula provided by Pengwuino for each of the two events you end up with 2 equations in 2 unknowns (h and $\phi$). You know how to solve that.