# General calculation of the oscillation freq of a hydrogen molecule

• Kibbel
In summary, the conversation discusses the problem of finding the frequency of oscillation for a hydrogen molecule based on the interatomic bond strength of other atoms. The equation f = (1/T) = omega/2pi is used, where omega is calculated using the spring constant and mass of the object. The correct solution is found by using the reduced mass of the two hydrogen atoms, resulting in a frequency of approximately 1.4965e14 cycles/s. Assistance is requested in verifying the solution.
Kibbel

## 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?

The mass in the equation ##f = \frac{1}{2 \pi}\sqrt{K/m}## should be the reduced mass of the two hydrogen atoms.

## 1. What is the oscillation frequency of a hydrogen molecule?

The oscillation frequency of a hydrogen molecule is approximately 1.4 x 10^15 Hz. This means that the molecule undergoes 1.4 trillion oscillations per second.

## 2. How is the oscillation frequency of a hydrogen molecule calculated?

The oscillation frequency of a hydrogen molecule can be calculated using the equation f = 1 / (2π√(m/k)), where f is the frequency, m is the reduced mass of the molecule, and k is the force constant of the bond between the two atoms.

## 3. What is the reduced mass of a hydrogen molecule?

The reduced mass of a hydrogen molecule is approximately half the mass of a single hydrogen atom, as the two atoms are of equal mass. This means that the reduced mass is approximately 1.67 x 10^-27 kg.

## 4. How does the oscillation frequency of a hydrogen molecule change with temperature?

The oscillation frequency of a hydrogen molecule increases with temperature, as the atoms have more kinetic energy and vibrate faster. However, this change is relatively small and can only be observed at very high temperatures.

## 5. What factors can affect the oscillation frequency of a hydrogen molecule?

The oscillation frequency of a hydrogen molecule can be affected by the mass of the atoms, the strength of the bond between them, and the temperature of the molecule. It can also be affected by external factors such as pressure or the presence of other molecules nearby.

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