Photon and Electron Collision

[Phoenixtears]

Homework Statement

An incident photon having a frequency of 2.00 E10^19 Hz collides with an electron initially at rest.

What is the total energy of the two-particle system after the collision? (In joules

The Attempt at a Solution

I've stared at this problem for at least an hour an have no idea where to go from here. Can anyone give me a leg up on this one. It feels like there isn't enough given information to even begin this... no velocity, no wavelength.

Thanks in advance!

~Phoenix

 

[whybother]

Well, to be fair... it's a photon, so you know the velocity (ie. the speed of light), and since you have the frequency, you have the wavelength - perhaps you can see it from there?

 

[nlightner]

As a scientist, it is important to approach this problem by using the principles of conservation of energy and momentum. The energy of a photon can be calculated using the formula E = hf, where h is Planck's constant and f is the frequency. In this case, the energy of the photon is 2.00 x 10^19 Hz x 6.63 x 10^-34 Joule seconds = 1.33 x 10^-14 Joules.

Since the electron is initially at rest, its initial momentum is zero. After the collision, the total momentum of the system must remain the same. Therefore, we can set up the equation:

Initial momentum of photon = Final momentum of photon + Final momentum of electron

Since the photon has no mass, its momentum is equal to its energy divided by the speed of light (p = E/c). Therefore, the equation becomes:

(1.33 x 10^-14 Joules)/c = Final momentum of photon + Final momentum of electron

To solve for the final momentum of the electron, we can use the equation p = mv, where m is the mass of the electron and v is its velocity. Since we are given the initial conditions of the electron (initially at rest), we can set the initial momentum to zero. Therefore, the equation becomes:

0 = Final momentum of photon + (mass of electron)(final velocity of electron)

Rearranging the equation, we get:

Final momentum of photon = -(mass of electron)(final velocity of electron)

Substituting this into our previous equation, we get:

(1.33 x 10^-14 Joules)/c = -(mass of electron)(final velocity of electron) + Final momentum of electron

Now, we need to use the fact that the total energy of the system is conserved. This means that the sum of the initial energy (1.33 x 10^-14 Joules) must equal the sum of the final energies. The final energy of the photon is given by E = hf, and the final energy of the electron is given by E = 1/2 mv^2. Therefore, our final equation becomes:

(1.33 x 10^-14 Joules) = (hf) + (1/2 mv^2)

Substituting in the values for h, f, and m, we get:

(1.33 x 10^-14 Joules) = (