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