Calculate DeBroglie Wavelength & Kinetic Energy of Electron

[SGL18]

Homework Statement

What is the DeBroglie wavelength of an electron whose energy is (a) 1.0eV (b) 100eV?
What is the kinetic energy in eV of an electron whose DeBroglie wavelength is that of visible red light at 650nm?

Homework Equations

λ=h/p = h/mv h = Planck's constant mv = particle

The Attempt at a Solution

 

[Sebastian]

Well, what have you tried? Where did you get stuck?

 

[SGL18]

i used the formula λ=h/(Em)^1/2 and correctly got 1eV to equal 1.23x10^-9.
For 100eV would i just multiply 100 by 1.6x10^-19? then plug it back into the equation?

 

[Redbelly98]

That should work.

Did you really mean to use p=(Em)^1/2 or is that a typo -- there is a missing number in the expression?

 

[paranormal]

To calculate the DeBroglie wavelength of an electron, we use the equation λ = h/mv, where h is Planck's constant, m is the mass of the electron, and v is its velocity. We can use the formula E = 1/2mv^2 to find the kinetic energy of the electron.

(a) For an electron with an energy of 1.0eV, we can find its velocity using the formula E = 1/2mv^2. Rearranging the equation, we get v = √(2E/m) = √(2*1.0eV/9.11*10^-31 kg) = 5.93*10^6 m/s. Plugging this value into the DeBroglie wavelength equation, we get λ = h/mv = (6.63*10^-34 J*s)/(9.11*10^-31 kg * 5.93*10^6 m/s) = 1.22*10^-10 m.

(b) For an electron with an energy of 100eV, we can follow the same steps as above to find its velocity, which comes out to be 1.88*10^7 m/s. Plugging this value into the DeBroglie wavelength equation, we get λ = h/mv = (6.63*10^-34 J*s)/(9.11*10^-31 kg * 1.88*10^7 m/s) = 3.68*10^-11 m.

To find the kinetic energy of an electron with a DeBroglie wavelength of 650nm, we can use the formula λ = h/mv and rearrange it to find v. Plugging in the known values of h, m, and λ, we get v = h/mλ = (6.63*10^-34 J*s)/(9.11*10^-31 kg * 650*10^-9 m) = 1.95*10^6 m/s. Then, using the formula E = 1/2mv^2, we can find the kinetic energy to be E = 1/2 * 9.11*10^-31 kg * (1.95*10^6 m/s)^2 = 1.78*10^-19 J, which is equivalent to 1.11 eV.

In summary,