Wavelength of Electron questions

[wikidrox]

1. I need some clarification that I answered this question properly

What is the wavelength of an electron of energy 5.0 eV?

Would I just use E=mc^2 to find the mass and then wavelength = h / mv to find the wavelength?

2. This question is also giving me problems

By what potential difference must a proton (Mo = 1.67 * 10^-27 kg) be accelerated to have a wavelength of 0.0011 nm?

Would I first use v = h / m * wavelength to find the velocity? And then
eV = 1/2 mv^2 to find the voltage?

 

[jdavel]

You could go right to the relativistic equation for the total energy of the electron, then get the relativistic momentum, and then use the deBroglie equation relating momentum and wavelength. But you won't learn much that way.

I'd start off by using the equation for kinetic energy to see how fast a 5eV electron is going. If that equation gives you an answer anywhere near the speed of light (3E8 meters/sec) then you'll have to back up and use something else. But if it doesn't, you'll be able to get the momentum by knowing the mass of the electron, and from there you can get the deBroglie wave length.

 

[M98Ranger]

1. Yes, you are correct in using the equations E=mc^2 and wavelength = h/mv to find the wavelength of an electron with an energy of 5.0 eV. Just make sure to convert the energy from electron volts to joules before plugging it into the equation.

2. Your approach is correct for finding the potential difference needed to accelerate a proton to a specific wavelength. First, use the equation v = h/mwavelength to find the velocity, then use the equation eV = 1/2 mv^2 to find the voltage. Remember to convert the mass from kilograms to grams before plugging it into the equation.