Equation for the energy of an particle oscillator?

In summary, the effective spring stiffness of an atom according to the Einstein model is 2ks,i, but in an example problem, it is stated that the energy of an oscillator with an interatomic spring stiffness of 5N/m with 5 quanta is given by \hbar \times \sqrt(\frac{4(5)}{\mathrm{weight of atoms}}). However, it should actually be \hbar \times \sqrt(\frac{2(5)}{\mathrm{weight of atoms}}). If this is difficult to understand, the standard equation involving Planck's constant and the effective interatomic spring stiffness of an oscillator is E = nh\sqrt(k/m).
  • #1
AATroop
31
2
So, my book claims that the effective spring stiffness of an atom (according to the Einstein model) is 2ks,i, but in an example problem they state one quantum of energy for an oscillator with an interatomic spring stiffness of 5N/m with 5 quanta is
[itex]\hbar \times \sqrt(\frac{4(5)}{\mathrm{weight of atoms}})[/itex]

But, shouldn't it be

[itex]\hbar \times \sqrt(\frac{\Huge{2}(5)}{\mathrm{weight of atoms}})[/itex]

If it's too difficult to understand, could someone just provide the standard equation involving Planck's constant[itex]/2\pi[/itex] and the effective interatomic spring stiffness of an oscillator?
 
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  • #2
The equation for the energy of an oscillator with an interatomic spring stiffness of k is given by: E = nh\sqrt(k/m),where n is the number of quanta, h is Planck's constant, and m is the mass of the oscillator.
 

Related to Equation for the energy of an particle oscillator?

1. What is an oscillator and how does it relate to energy?

An oscillator is a physical system that exhibits periodic motion or vibrations. The energy of an oscillator is directly related to its motion, with the maximum energy occurring at the extremes of the motion and the minimum energy occurring at the equilibrium point.

2. What is the equation for the energy of a particle oscillator?

The equation for the energy of a particle oscillator is E = (n + 1/2)hν, where E is the energy, n is the quantum number, h is Planck's constant, and ν is the frequency of the oscillator.

3. How does the energy of an oscillator change with the quantum number?

The energy of an oscillator increases with the quantum number, meaning that as the quantum number increases, the energy levels of the oscillator also increase. This is due to the fact that the higher the quantum number, the higher the energy level of the oscillator.

4. What is the significance of Planck's constant in the equation for the energy of an oscillator?

Planck's constant, denoted by h, is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. In the equation for the energy of an oscillator, Planck's constant is used to calculate the energy levels of the oscillator based on its frequency.

5. Can the equation for the energy of an oscillator be applied to all types of oscillators?

Yes, the equation for the energy of an oscillator can be applied to all types of oscillators, as long as they exhibit periodic motion and have discrete energy levels. This includes simple harmonic oscillators, as well as more complex systems such as molecular vibrations and electronic oscillations.

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