How to Determine n for Quantized Energies in a Pendulum?

In summary, the conversation discusses finding the value of n for a simple pendulum with a length of 0.6 m and a bob with a mass of 0.5 kg, in order for En+1 to exceed En by 0.010 percent. The equation used is En=(n+1/2)hf0, and a revised approach is suggested where En+1=En*1.0001, resulting in a value of n=9999.5, rounded up to 10000.
  • #1
w3390
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Homework Statement



A simple pendulum has a length equal to 0.6 m and has a bob that has a mass equal to 0.5 kg. The energy of this oscillator is quantized, and the allowed values of energy are given by En = (n + 1/2)hf0, where n is an integer and f0 is the frequency of the pendulum. Find n such that En+1 exceeds En by 0.010 percent.

Homework Equations



En=(n+1/2)hf0

The Attempt at a Solution



I thought this sounded like a simple algebra problem, so I set .0009(En+1)=En and solved for n after plugging in the equations. I know there is something wrong with this equation because I keep getting negative, non-integer values for n but I cannot figure out what is wrong. Any help is greatly appreciated.
 
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  • #2
Since my first post, I have tried a revised approach. This time I have En+1=En*1.0001. This gives me (n+1)+(1/2)=(n+(1/2))1.0001. After doing all the algebra, I am getting 9999.5 as my answer for n. Since the question asks for an integer value, I do not know if show input 9999 as my answer or if my answer is just wrong in general.
 
  • #3
Your second method looks fine, and I would round 9999.5 up to 10000.:approve:
 

FAQ: How to Determine n for Quantized Energies in a Pendulum?

1. What is "n" in quantized energies?

In quantum mechanics, "n" represents the principal quantum number, which is used to describe the energy levels of an atom. It determines the size and energy of the electron's orbit around the nucleus.

2. How is "n" related to quantized energies?

The value of "n" directly corresponds to the energy level of an electron in an atom. As "n" increases, the energy level also increases, resulting in a higher energy state for the electron.

3. How do you find the value of "n" for quantized energies?

The value of "n" can be found using the Rydberg formula, which relates the energy level of an electron to the wavelength of light emitted or absorbed by an atom. "n" can also be determined by considering the electron's energy in relation to the energy of the atom's nucleus.

4. Why is "n" important in quantized energies?

The value of "n" is important because it helps to explain the discrete energy levels of atoms, as opposed to the continuous energy levels predicted by classical physics. It also plays a crucial role in understanding the behavior and properties of atoms and molecules.

5. Can "n" have any value in quantized energies?

No, "n" can only have positive integer values. The lowest possible value for "n" is 1, which corresponds to the ground state of an atom. Higher values of "n" represent excited states of the atom with increasing energy levels.

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