An electron traveling at a speed of

[atoreta88]

Homework Statement

An electron traveling at a speed of 6.0 x10^7 m/s. strikes the target of an x-ray tube. Upon impact, the electron decelerates to 1/4th of its original speed, emitting an x-ray in the process. What is the wavelength of the x-ray photon?

Homework Equations

I think I'm suppose to use the formula E=hf (eqn 1) and v=lambda*f (eqn 2)

The Attempt at a Solution

I manipulated both equations (eqn 1 and eqn 2) to get the formula E=(h*v)/(lambda), but that leaves me with two unknowns..when all I want is lambda to be the only unknown. I'm not sure how I would find the energy...and I'm not sure if I'm even using the correct formulas. Hopefully I'm on the right track?

 

[graphene]

What you want is the wavelength of the X-ray - an EM wave. What is its speed ?

 

[praveenpp]

we can find the wavelength of the emitted x-ray photon. using

first find the kinetic energy of the electron using K.E = 1/2 m*v^2.
then apply the formula

lambda = (h*v)/K.E

it will give the answer for you.

 

[berkeman]

we can find the wavelength of the emitted x-ray photon. using

first find the kinetic energy of the electron using K.E = 1/2 m*v^2.
then apply the formula

lambda = (h*v)/K.E

it will give the answer for you.

That is incorrect. Even a dimensional analysis shows that there is something wrong with that equation.

And please do not do the original poster's (OP's) work for them -- they are required to do the work themselves. You may provide hints and ask questions, in order to help them figure out the problem on their own.

 

[rwisz]

As a scientist, let me help you with this problem. First, let's start by identifying the known values and the unknown value in this problem. The known values are the initial speed of the electron (6.0 x10^7 m/s), the final speed of the electron (1/4th of its original speed), and the fact that an x-ray is emitted in the process. The unknown value is the wavelength of the x-ray photon.

Next, let's recall some important principles from physics. When an electron decelerates, it loses energy. This lost energy is then converted into electromagnetic radiation, in this case, an x-ray photon. We can use the principle of conservation of energy to solve this problem. This principle states that energy cannot be created or destroyed, only transferred from one form to another. So, the energy lost by the electron will be equal to the energy gained by the x-ray photon.

Now, let's use the formula for kinetic energy (KE=1/2mv^2) to find the initial kinetic energy of the electron. We know the mass of an electron (9.11 x 10^-31 kg) and its initial speed (6.0 x10^7 m/s), so we can calculate its initial kinetic energy to be 1.64 x 10^-15 J.

Next, let's use the principle of conservation of energy to find the energy of the x-ray photon. We know that the energy lost by the electron (1.64 x 10^-15 J) will be equal to the energy gained by the x-ray photon. So, we can use the formula E=hf (where h is Planck's constant and f is the frequency) to find the energy of the x-ray photon.

Now, we need to find the frequency of the x-ray photon. We can use the formula v=lambda*f (where v is the speed of light, lambda is the wavelength, and f is the frequency) to find the frequency. We know the speed of light (3.00 x 10^8 m/s) and the final speed of the electron (1/4th of its original speed), so we can calculate the frequency to be 1.5 x 10^16 Hz.

Finally, we can use the formula E=hf to find the energy of the x-ray photon. Plugging in the known values, we get E=(6.63 x 10^-34