How Fast Would a Nitrogen Molecule Travel with Photon Energy?

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SUMMARY

The discussion centers on calculating the speed of a nitrogen molecule (N2) when it possesses energy equivalent to that of a photon across various wavelengths, specifically 1.000E4 nm, 500 nm, 100 nm, and 0.10 nm. Participants suggest using the equation E = hc/lambda to determine the energy of the photon, followed by applying the kinetic energy formula KE = (1/2)mv^2 to solve for velocity. There is uncertainty regarding the relevance of the RMS speed equation Vrms = (3kT/m)^(1/2) in this context, as it may not directly apply to the problem at hand.

PREREQUISITES
  • Understanding of the kinetic energy formula KE = (1/2)mv^2
  • Familiarity with the energy-wavelength relationship E = hc/lambda
  • Knowledge of the concept of photon energy and its calculation
  • Basic grasp of the RMS speed equation Vrms = (3kT/m)^(1/2)
NEXT STEPS
  • Explore the derivation and applications of the kinetic energy formula KE = (1/2)mv^2
  • Learn about the relationship between energy and wavelength in electromagnetic radiation
  • Investigate the de Broglie wavelength equation lambda = h/p and its implications for particle velocity
  • Study the concept of root mean square (RMS) speed in gases and its relevance in thermodynamics
USEFUL FOR

This discussion is beneficial for students in physical chemistry, particularly those studying molecular speed and energy relationships, as well as educators seeking to clarify concepts related to photon energy and molecular dynamics.

solsek
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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?
 
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solsek said:
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 vrms equation :confused:
 

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