What Could Be Wrong with My Calculations in the Infinite Potential Well Problem?

• Meekay
In summary, the conversation discusses finding the ground state energy and transition energy of an electron in an infinitely deep potential well, using equations such as E_1 = \frac{pi^2 (hbar c)^2}{2M_e C^2 a^2}. The calculated values for E1 and the transition energy are 26.02 eV and 130.13 eV respectively. However, there is some uncertainty about the wavelength of the emitted photon, with a calculated value of 9.53 nm which seems too small. Further calculations using hc = 1239.8 eV.nm and mc^2 = 511000 eV confirm the initial results.
Meekay
three parts to this one, I can't seem to justify my values, units cancel, but the numbers don't seem right. I think I may have used a wrong equation for part B but I don't know what else to use.

Problem: An electron is confined to an infinitely deep potential well of width 0.120 nm.
a.) Calculate its ground state energy, E1
b.)If the electron makes a transition from the n=3 state to the n=2 state, how much energy is carried away by the emitted photon?
c.)What is the wavelength of this photon?equations:

a.) $$E_1 = \frac{pi^2 (hbar c)^2}{2M_e C^2 a^2}$$

b.) $$E_\gamma = E_3 - E_2$$

c.) $$\lambda = \frac{hc}{E_\lambda}$$My attempt:

a.) using hbar*c = 197 ev*nm and MeC^2 = 511000 ev i get a value of 26.02ev for E1

b.) using the same equation as above for the n=3 and n=2 states and subtracting I get 130.13ev

c.) using hc = 1240 ev*nm I get an answer of 9.53 nm which doesn't seem right to me. I feel like the photon should have a larger wavelength.

Why do you think the photon should have a bigger wavelength?

Lets see - using ##h= 2\pi \hbar## ;$$E_n=\frac{n^2(h c)^2}{8mc^2a^2}=n^2E_1$$ (when you use LaTeX, put a backslash in front of the symbol name so \hbar renders as ##\hbar## etc.)

hc=1239.8 eV.nm
mc^2=511000 eV
a=0.120nm

Looks good to me:
Go through the arithmetic one step at a time, make sure you have squared the correct terms.

What is an Infinite Potential Well?

An infinite potential well is a theoretical model used in quantum mechanics to study the behavior of particles confined within a specific region of space with impenetrable walls.

What is the significance of an Infinite Potential Well in quantum mechanics?

The infinite potential well model helps us understand the quantization of energy levels in a confined system, as well as the wave-like behavior of particles.

How does the size of the Infinite Potential Well affect the particle's behavior?

In an infinite potential well, the size of the well determines the allowed energy levels and the probability of finding the particle in different regions within the well. A larger well will have more energy levels and a lower probability of finding the particle at the edges.

Can a particle escape from an Infinite Potential Well?

No, the walls of an infinite potential well are considered impenetrable in this model, so the particle cannot escape from the well.

What are the limitations of the Infinite Potential Well model?

The infinite potential well model is a simplified and idealized representation of a physical system. It does not take into account real-world factors such as interactions with other particles or the effects of external fields. It is also limited to one-dimensional systems and cannot fully describe the behavior of particles in three-dimensional space.

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