Orbital Frequency of an electron in a hydrogen atom

In summary, the conversation discusses the classical model of the hydrogen atom and the calculations involved in finding the electron's orbital frequency and effective current. The main equations used include the relationship between frequency, wavelength and the speed of light, as well as the equations for force, momentum, and current. The final solution involves dividing the circumference by the velocity to find the orbital period, and then taking the reciprocal to find the orbital frequency.
  • #1

Homework Statement



In a classical model of the hydrogen atom, the electron moves around the proton in a circular orbit of radius 0.053 nm.

What is the electron's orbital frequency?

What is the effective current of the electron?


Homework Equations



Freq * Wavelength = Speed of light
(V*lambda = c)

Lambda = (plancks constant)/momentum

momentum = (mass of electron)*(Velocity)

F = qE = m(v^2)/R

current...I = q*ie...(charge of electron)*(electron current)

number of electrons...Ne = ie*delta_t...(electron current)*(period I presume)

Ne = 1

The Attempt at a Solution



Mass of electron = 9.1094*10^-31 kg
qe- = -1.6*10^-19 coulombs
radius = 0.053*10^-9 m

...utlizing this information I found the velocity from the Force equation, deriving:
sqrt(K(q^2)/(r*me-) = v

Then plugged in velocity into the equation: lambda = h/(mv)

Plugged lambda into: V = c/lambda

...finding my frequency to be about 900*10^15 Hz...but this was wrong. Help would be extremely appreciated!
 
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  • #2
RichardEpic said:
Freq * Wavelength = Speed of light
(V*lambda = c)

This is the equation for the frequency of a light wave, which is not really relevant here.

The question is asking you for the orbital frequency of the electron i.e. how often does a full cycle (orbit) repeat?

Well, the orbital frequency is just the reciprocal of the orbital period. How do you figure out the orbital period? It's as simple as remembering that distance = speed*time. What distance is covered by the electron in one orbit?
 
  • #3
ohhh...well, I overthunk it. Lol! So, take the velocity I found, and divide it into the circumference: (2*pi*r)/v = seconds...in other words the period. THANKS! It worked!
 

1. What is the formula for calculating the orbital frequency of an electron in a hydrogen atom?

The formula for calculating the orbital frequency of an electron in a hydrogen atom is f = (1/2π)(1/n^2)√(k/me), where f is the orbital frequency, n is the principal quantum number, k is the Coulomb's constant, and me is the mass of the electron.

2. How does the orbital frequency of an electron in a hydrogen atom vary with the principal quantum number?

The orbital frequency of an electron in a hydrogen atom is directly proportional to the inverse of the principal quantum number. This means that as the principal quantum number increases, the orbital frequency decreases.

3. What is the significance of the orbital frequency of an electron in a hydrogen atom?

The orbital frequency of an electron in a hydrogen atom is significant because it determines the energy and stability of the electron in its orbit. It also plays a role in the spectral lines and energy levels of hydrogen atoms.

4. How does the mass of the electron affect the orbital frequency in a hydrogen atom?

The mass of the electron has an inverse relationship with the orbital frequency of an electron in a hydrogen atom. This means that as the mass of the electron increases, the orbital frequency decreases.

5. Can the orbital frequency of an electron in a hydrogen atom be measured?

Yes, the orbital frequency of an electron in a hydrogen atom can be measured through spectroscopy techniques. By analyzing the spectral lines of hydrogen, the frequency of the electron's orbit can be determined. Additionally, theoretical calculations can also be used to determine the orbital frequency.

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