What is velocity of electron?

Question

If electron has momentum p, then
its waveleghth is λ=h/p,
and its frequency is f = E/h.

The velocity of de Broglie wave is
u = λf = h/p E/h = E/p = 1/2 p²/m /p = 1/2 p/m.

Should not velocity of electron be v = p/m?

Answer 1

Excellent question!

Answer: no, the u that you are calculating is not the classical momentum of the particle: it is the phase velocity of the wave. The classical momentum of the particle is the *group velocity* of a wave packet, which turns out to be p/m, but the analysis takes about one week of a QM class.

Answer 2

Velocity Of Electron

Answer 3

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RE:
What is velocity of electron?
If electron has momentum p, then
its waveleghth is λ=h/p,
and its frequency is f = E/h.

The velocity of de Broglie wave is
u = λf = h/p E/h = E/p = 1/2 p²/m /p = 1/2 p/m.

Should not velocity of electron be v = p/m?

Answer 4

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First of all, matter cannot move at the speed of light. If something has a rest mast -- if, when stopped, its mass is not zero, then it's called matter and you most definitely cannot have it moving at a speed of light. It would take infinite energy to do so. That we know from special relativity. So light speed is out of question here. The model where electrons "orbit" the atom has this fatal flaw that there's no such thing as orbital velocity of an electron that's bound to an atom. You will find more about it in the first reference I list. In a conductor, not all electrons participate in conduction. Some don't and are quite "firmly" bound to the atoms. Then, some electrons from each atom form the electron gas that is mobile and constitutes the charge that can move around as current. Those electrons are called mobile electrons. They always move around -- they do behave like an electron gas. Do you recall kinetic gas model? The molecules of air happily bouncing around, slamming into each other and into other things? Same happens, more or less, with mobile electrons in a conductor. The electron gas, just like ideal gas, has some average electron velocity: it's known as the drift velocity. When there is no current flow, the movement of electrons averages to be zero: if you imagine a slice across a piece of copper wire, the electrons passing the slice through to the left equal in number the electrons passing through to the right. Net flow is zero. As if you stirred water in a like: it doesn't go anywhere, just flows around. Now recall that electrical current in say a wire is simply how much charge has moved into/out of that wire in a given time: current = charge / time Now knowing that electrons have a drift velocity, and knowing their density, we can express the current as: current = electron density * cross section of the conductor * drift velocity * unit charge of an electron Let's look at the units: electron density = 1 / volume = 1 / distance^3 cross section = area = distance ^ 2 drift velocity = distance / time unit charge = charge [electron density * cross section] = 1 / distance [1/distance * drift velocity] = 1 / time [1/time * unit charge] = charge / time So, knowing the current, the wire's cross section, the unit charge of electron, and electron density, we can easily come up with the drift velocity: drift velocity = current / (electron density * cross section * unit charge) I leave it as an exercise for you to figure out drift velocity in say copper. All the numbers are in the references I provided below. Make sure you read through those references, perhaps leaving special relativity aside for a moment.

Answer 5

The Electron oscilliatory orbit occurs around the nucleus of the Hydrogen atom.
The orbit has a constant angular velocity,which is equal to Planck's constant = h
PLanck constant equates to the product of the average energy of the electron around the orbit and the period of oscillation around the orbit.The dimension is Kg m^2/sec.

The procuct of a variable Electron Mass and its velocity ,and its orbital radius vector equal a constant angular velocity.
That means that the mass and velocity of the electron is not constant as it orbirts the Nucleus of the Atom.

The equation for angular momentum is as follows;

Mi x Vi x R = h
where Mi is =the value of the electron mass at that instant.
Vi is =the value of the electron's speed at that instance.
R is= the radius vector of the electron at the same instance.

The instantaneous Velocity of the electron is calculated as follows;

Vi =h/ Mi x lamda.

where lamda is the wave lenght of the Electron.

The velocity of an unbound constant mass electron is caculated as follows;

Energy of the free electron divided by its constant mass equals the velocity square of the electron. or it can be calculated as follows;

E=Me x lamda ^2 x fq ^2

Where Me is the mass of the electron and lamda is the wave lenght and fq is the frequency of the electron as it oscillates during its motion.

So the velocity of the Free electron is=Lamda x fq.
The Linear momentum of the electron equals=Me xlamda x fq.
Or P=Me x Va
P= momentum,Va =average velocity .
Therefore Va = P/Me.

Your assumption is correct ,but the velocity of the free Electron is an average velocity.

Note ; Niels Bohr made the angular momentum of the electron in the hydrogen Atom ,as a multiple of planck's constant. However; where he went wrong is because he forgot that the electron's mass is variable within the atom as a function of temperature.

Very vely simple

Answer 6

it would be if you were talking about a ball, but it's an electron!

showing how an electron is not a ball earned him a nobel prize!

Answer 7

Speed o' light - 186,000 mps