Calculating Energy of Photoelectrons Ejected from a Magnesium Surface

[euphoriax]

Homework Statement

A magnesium surface has a work function of 3.68 eV. Electromagnetic waves with a 215 nm wavelength strikes the surface and eject photoelectrons. Calculate the energy of the photoelectrons in Joules and in electron volts.

W= 3.68 eV = 5.96x10^-19 J
wavelength= 215 nm = 2.15x10^-7 m
E=?
h= 6.63x10^-34 J.s
c= 3.00x10⁸ m/s
m_electron= 9.1x10^-31 kg

Homework Equations

v=f(wavelength)
E=hf-W

The Attempt at a Solution

v= f(wavelength)
f= v/wavelength
f= (3.0x10⁸ m/s)
f= 1.39x10¹⁵ hz

E= hf-W
= (6.63x10^-34 J.s) (1.39x10¹⁵ Hz) - 5.96x10^-19 J)
E=3.29x10^-19 J
E= 2.03 eV

The answer that I got is wrong. The real answer is supposed to be 3.35x10^-19 J, and 2.09 eV. Does anyone know where I went wrong? If you do, I would appreciate if you could explain it too
Thank you!

 

[0ddbio]

You are doing it right, you are just getting rounding errors I believe.

Try writing it all out into one big equation. without substituting any numbers. Then just put all of the numbers in at the same time for one calculation at the end, this will be more accurate.
I just did it the same way you did and got 2.09eV

 

[euphoriax]

Oh, that's true.
thank you!