General calculation of the oscillation freq of a hydrogen molecule

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SUMMARY

The discussion centers on calculating the oscillation frequency of a hydrogen molecule (H2) using the formula f = (1/T) = ω/2π, where ω = √(K/m). The user initially attempted to use a spring constant from copper (20.6 N/m) and the mass of a hydrogen atom (1.674e-27 kg) but arrived at an incorrect frequency of 1.4965e14 Hz. The correct approach requires using the reduced mass of the two hydrogen atoms for accurate results. This highlights the importance of using the correct mass in oscillation frequency calculations.

PREREQUISITES
  • Understanding of harmonic oscillators and spring constants
  • Familiarity with the concept of reduced mass in two-body systems
  • Knowledge of basic physics equations related to oscillation frequency
  • Ability to perform calculations involving scientific notation
NEXT STEPS
  • Calculate the reduced mass of two hydrogen atoms for accurate frequency determination
  • Research the concept of interatomic forces and their relation to spring constants
  • Explore the derivation of the oscillation frequency formula f = (1/2π)√(K/m)
  • Investigate the physical properties of hydrogen molecules and their vibrational modes
USEFUL FOR

Students studying quantum mechanics, physicists interested in molecular vibrations, and educators teaching concepts related to oscillation and molecular dynamics.

Kibbel
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Homework Statement



Okay here's the problem, normally I can get all this stuff, but right now this is blowing my mind, partly because its too general.

"In other problems and examples in the textbook we found the effective spring stiffness corresponding to the interatomic force for aluminum and lead. Let's assume for the moment that, very roughly, other atoms have similar values.

(a) What is the (very) approximate frequency f for the oscillation ("vibration") of H2, a hydrogen molecule containing two hydrogen atoms? Remember that frequency is defined as the number of complete cycles per second or "hertz": f = 1/T. There is no one correct answer, since we're just trying to calculate the frequency approximately. However, just because we're looking for an approximate result doesn't mean that all answers are correct! Calculations that are wildly in disagreement with what physics would predict for this situation will be counted wrong.
f = _____cycles/s (hertz)"

Homework Equations



im using f = (1/T) = omega/2pi

and omega = sqrt(K/m), K being the spring constant, (or interatomic bond strength) and m being the mass of the object


The Attempt at a Solution



okay well first of all I just went and looked up the real answer because we never actually calculated the spring stiffness for aluminum or lead earler.

I put in, 8.03e14 cycles/s (hertz), but apparently the real answer is incorrect.

So I look in the textbook, and we have solved to find the interatomic bond strength of copper atoms, which was 20.6 N/m. So then I did

f = sqrt(K/m)/2*pi

sqrt(29.6/(2*1.674e-27))/(2*pi)

1.674e-27 being the mass of a hydrogen atom.

So I got 1.4965e14, which again was wrong!

Can someone help me out?
 
Physics news on Phys.org
The mass in the equation ##f = \frac{1}{2 \pi}\sqrt{K/m}## should be the reduced mass of the two hydrogen atoms.
 

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