How Fast Would a Nitrogen Molecule Travel with Photon Energy?

[solsek]

Homework Statement

Consider a gas-phase N2 molecule. It's RMS speed is given by

Vrms = (3kT/m)^(1/2)

What speed would the gas molecule have if it had the same energy as a photon of the following wavelengths of IR, visible, UV and X-Ray electromagnetic radiation?

lambda = 1.000E4nm, 500nm, 100nm, 0.10nm

Homework Equations

E=hc, E=hc/lambda E = (mv^2)/2 , not sure if we should use lambda = h / p (momentum)

The Attempt at a Solution

So I don't know how to use the Vrms equation that is given in the problem. I am not sure if we need to use it at all (Btw, this in the first problem set of my pchem class so it should be pretty easy, I am just not sure if I am doing it right).

E = hc/lambda, using this equation we can find the energy of the gas molecule if it had the wavelength given in the problem.

Once we find the energy E we can use KE = 1/2mv^2 to some for v.

I am not sure if we are supposed to use this method or use the Debroglie equation where lambda = h / mv and solve for velocity that way.

Any thoughts?

 

[Redbelly98]

E = hc/lambda, using this equation we can find the energy of the gas molecule if it had the wavelength given in the problem.

Once we find the energy E we can use KE = 1/2mv^2 to some for v.

That is how I would solve it. Not sure why they bothered with the v_rms equation

 

[Blueshift5]

Your approach is correct. You can use the formula E=hc/lambda to find the energy of the photon for each given wavelength. Then, using the formula E=(mv^2)/2, you can solve for the velocity of the gas molecule. This approach is valid and will give you the correct answer. Alternatively, you can also use the Debroglie equation where lambda = h/mv and solve for velocity. Both methods will give you the same answer. It's good to explore and use different equations to solve a problem, so you can choose whichever method you feel more comfortable with.