When you illuminate a surface, electrons receive energy in the form #E=hf# from the photons of light, where #h# is Planck's constant and #f# is frequency (of light), and fly away with a kinetic energy #1/2m_ev^2#. The problem is that the electron is bound to its atom! We represent this situation by basically saying that if you give an energy to the electron UP TO #E_T=hf_T# where #f_T# is the threshold frequency the electron will not bulge.
So:
#"Kinetic Energy"="incoming Photon Energy"-"Energy of binding"#
the last one is normally called Work Function or energy needed for the electron to extricate itself from the atom:
So we can write (in numbers) for our electron:
#1/2m_ev^2=hf-hf_T#
#1/2(9.1xx10^-31)(1.06xx10^6)^2=6.63xx10^-34f-(6.63xx10^-34*5.51xx10^14)#
rearranging:
#1/2(9.1xx10^-31)(1.06xx10^6)^2=6.63xx10^-34(f-5.51xx10^14)#
#f=1.32xx10^15s^-1#
This is the required frequency. It can be converted into wavelength as:
#lambda=c/f=(3xx10^8)/(1.32xx10^15)=2.27xx10^-7m#
[#c# is the speed of light in vacuum]
