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### Worked Example

Posted: Sun Jul 02, 2017 11:44 pm
I'm going through the "The Quantum World" notes in the course reader and after reviewing the first worked example:
"The following questions relate to the same metal used in a series of photoelectric experiments.
If 3.61 x 10^-19 J is required to remove an electron with zero kinetic energy from a metal surface, what would be the longest wavelength light that could do this?" I don't remember how combining E = hv and c = λv gives E = hc/λ. How do you reach that final formula (E = hc/λ) in order to solve for the wavelength?

### Re: Worked Example

Posted: Mon Jul 03, 2017 2:00 pm
Here are your two equations to combine:

You set the speed of light equation to equal velocity:

Then, you see that has velocity in it, so you can plug the velocity from the previously solved equation^ into the velocity in the energy equation.

Yay! We have that equation, now we can conquer the world or solve the rest of the question.

Goal: You want to find the wavelength using the equation: and we are given the energy of the incident light (3.61 x 10^-19 J).

1) You can rearrange the equation to soluve for wavelength:

2) Now, you have the energy, planck's constant, and speed of light constant to solve for wavelength. Plug and chug:

3)**Sometimes you would multiply the wavelength by 10^9 m to convert meters to nanometers for convenience.

Rejoice!