Finding work function from two light sources with different wavelengths

[phy]

A light source of wavelength lambda illuminates a metal and ejects photoelectrons with a maximum kinetic energy of 1.00 eV. A second light source with half the wavelength of the first ejects photoelectrons with a maximum kinetic energy of 4.00 eV. What is the work functin of the metal?

I know I can use the equation for maximum kinetic energy defined by K=hf - phi where K is the maximum kinetic energy for emmitted electrons, h Planck's constant and f is frequency. Since we don't have frequency, I thought of rewriting the equation as K=hc/lambda - phi but now I don't know how to incorporate both light sources and to actually to solve for phi. Do I have to write two separate linear equations and solve them or is there something esle I'm supposed to be doing? Help please?

 

[Parth Dave]

You have the right idea. Two separate equations and solve them. Go with it.

 

[jtbell]

Do I have to write two separate linear equations and solve them

Bingo!

Any time you have two unknown quantities, you should suspect that you'll have to set up two equations for them, and solve them together.

 

[phy]

Haha I just reread the question. I think I was having another blonde moment just a little while ago. Thanks for your help guys