Photons and matter waves: The photon of quantum light: I need help

Homework Statement

How fast must an electron move to have a Kinetic Energy equal to the photon energy of sodium light at wavelength 590 nm.

Homework Equations

photon energ E =hf

h = 6.63 * 10 ^ -34 J * s = 4.14 = 10^-15 eV *s

f = c/ lamda

c = 3 * 10^ 8 m/s

mass of an electron is 9.11 * 10 ^ -31 (kg) or 511 keV

The Attempt at a Solution

Ok I solved for the energy of a photon for sodium light

E = 6.63 * 10 ^ -34 J *s * ( (3* 10 ^ 8 m/s) / 590 * 10 ^ -9 meters) = 1.989 * 10 ^ -25 Joules

Were solving for Velocity. How do I do this problem it's confusing.

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Pengwuino
Gold Member
Well you're looking for the kinetic energy (and thus velocity) right? Well $$E_{kinetic} = \frac{{mv^2 }}{2}$$ and you know the energy of the photon so equate them and find the velocity.

Sorry about that I'll make my information much clearer next time. So that's the equation I use.

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Would it be like this

$$v = \frac{{\sqrt{{2E }} \div {m} }$$

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Pengwuino
Gold Member
Yes, where E = hf = hc/lamda

So is that E of photon energy of soidum light the same as the kinetic energy

Check your math again. I get a different value for energy using the same numbers you gave as input.

so then it would be

It would be v = sqrt { 2 (3.37 * 10 ^ -19 joules / 8.19 * 10^ -14 joules}

m of electron in joules is 8.19 * 10 ^ -14 joules

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Oh yea the Enery of a photon for sodium light is actually
$$E = 3.371186441 \times 10^-19$$

That's what I got.

I got 2.86 * 10 ^ -3 m/s

That doesn't seem correct. Your equation for v doesn't look right, but I don't know if you are just typing in the tex code wrong. Did you really intend for the mass, m, to be in the numerator of that equation?

Also, I'm not sure where you are getting the mass of the electron in joules. If you are using SI units of joules for energy, then the electron mass should be in kg.

Pengwuino
Gold Member
Wait yes, your equation for the velocity in terms of the energy changed... its divided by m.

Well my last word on this...it looks like you threw another factor of c in there somewhere. If I divide the answer I get in meters/sec by 3*10^8 m/s, then I get the answer you posted above. So your answer would be correct if it was in units of "c".