Calculate the frequency of an electron traveling at

1.85 X 10^7 m/s.

Since the velocity and mass of the electron are known, I tried to use the De Broglie wavelength formula:

let L = lambda, h = plancks constant

L = h/mv
and I got 3.94*10^-11 for the wavelength
Since frequency is the inverse of wavelength I did
1 over that answer, but it's wrong.

I can't use E = hv (v being nu, frequency) because that applies only to photons.

What am I missing? What should I do?

You are correct that the De Broglie wavelength formula is applicable for calculating the wavelength of particles, including electrons. However, to calculate the frequency of an electron, you need to use the relativistic relationship between energy (E), mass (m), and velocity (v).

The relativistic relationship is given by:

E = γmc^2

where E is the total energy of the electron, m is its mass, c is the speed of light, and γ is the Lorentz factor defined as:

γ = 1 / sqrt(1 - (v^2 / c^2))

To calculate the frequency, we can connect energy and frequency using Planck's equation:

E = hf

where h is Planck's constant and f is the frequency.

First, we need to calculate the total energy of the electron using the relativistic relationship:

E = γmc^2 = (1 / sqrt(1 - (v^2 / c^2))) * mc^2

Substituting this into Planck's equation, we get:

f = E / h = [(1 / sqrt(1 - (v^2 / c^2))) * mc^2] / h

To calculate the frequency, you will need to know the mass of the electron (m) and the speed of light (c). The values for these constants are as follows:

m = 9.10938356 × 10^-31 kg (approximate)
c = 299,792,458 m/s (exact)

Once you substitute the appropriate values into the equation and perform the calculations, you should be able to find the frequency of the electron.

To calculate the frequency of an electron, you are on the right track by using the De Broglie wavelength formula. However, the equation you used to calculate the wavelength is incorrect. The correct formula for the De Broglie wavelength of a particle is:

λ = h / p

where λ is the wavelength, h is the Planck's constant, and p is the momentum of the particle.

The momentum of an electron is given by:

p = m * v

where m is the mass of the electron and v is its velocity.

In your case, the velocity of the electron is given as 1.85 x 10^7 m/s. The mass of an electron is approximately 9.11 x 10^-31 kg. Therefore, the momentum of the electron is:

p = (9.11 x 10^-31 kg) * (1.85 x 10^7 m/s) = 1.68 x 10^-23 kg·m/s

Now, we can calculate the wavelength using the De Broglie wavelength formula:

λ = (6.63 x 10^-34 J·s) / (1.68 x 10^-23 kg·m/s) ≈ 3.94 x 10^-11 m

Now that we have the wavelength, we can calculate the frequency by taking the inverse of the wavelength:

f = 1 / λ ≈ 1 / (3.94 x 10^-11 m) ≈ 2.54 x 10^10 Hz

Therefore, the frequency of the electron traveling at 1.85 x 10^7 m/s is approximately 2.54 x 10^10 Hz.

Here is a sample:https://socratic.org/questions/calculate-the-de-broglie-wavelength-of-an-electron-traveling-at-3-85-106m-s

when you find lambda, change that to frequency , f=speed/lambda