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In summary, a "Particle (infinite 1-D well)" is a simplified model in quantum mechanics that describes the behavior of a single particle confined within an infinitely deep potential well. The model is significant in understanding basic principles of quantum mechanics and is useful for solving more complex problems. The assumptions made in the model include an infinitely deep potential well, no external forces, rigid walls, and no spin or magnetic fields. The wave function in the model describes the probability of finding the particle at a specific position and can be used to calculate its energy. The energy of the particle is quantized and cannot exceed a maximum value known as the energy ground state.

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mss90

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## Homework Statement

If a particle (infinite 1-D well) in ground state n =1 with an energy 1.26 eV above E=0. Whats the energy needed to get it to 3rd excited state n =4?

## Homework Equations

## The Attempt at a Solution

any hints?

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- #2

ZetaOfThree

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You need to attempt the problem before we will help.

- #3

mss90

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Im thinking En = h2kn2/(2m) or En = n2π2ħ2/(2mL2)?

- #4

mss90

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m= 9.11E-31kg*ħ=h/2pi*

a=(pi2* ħ2/E2m)*12*

a=1.66E-34/2.3E-30

a= 7.22E-5eV

I tried this

- #5

HalfLostAndSearching

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The energy needed to get a particle in an infinite 1-D well to a specific excited state can be calculated using the formula E_n = (n^2 * h^2)/(8mL^2), where n is the quantum number of the state, h is Planck's constant, m is the mass of the particle, and L is the length of the well.

To get from the ground state n=1 to the 3rd excited state n=4, we can use the formula:

E_4 = (4^2 * h^2)/(8mL^2)

To find the energy difference, we can subtract the energy of the ground state from the energy of the 4th excited state:

E_4 - E_1 = [(4^2 * h^2)/(8mL^2)] - [(1^2 * h^2)/(8mL^2)]

= [(16 * h^2)/(8mL^2)] - [(1 * h^2)/(8mL^2)]

= [(15 * h^2)/(8mL^2)]

= 15/8 * (h^2)/(mL^2)

Therefore, the energy needed to get from the ground state to the 4th excited state is 15/8 times the energy of the ground state.

## Related to What Energy Is Needed to Reach the 3rd Excited State in an Infinite 1-D Well?

## What is a "Particle (infinite 1-D well)"?

A particle (infinite 1-D well) refers to a simplified model in quantum mechanics that describes the behavior of a single particle confined within an infinitely deep potential well. The particle is considered to have no external forces acting on it and is only allowed to move within the well along one dimension.

## What is the significance of the infinite 1-D well model?

The infinite 1-D well model is significant because it helps us understand the basic principles of quantum mechanics, such as the quantization of energy and wave-particle duality. It is also a useful tool for solving more complex problems in quantum mechanics.

## What are the assumptions made in the infinite 1-D well model?

The infinite 1-D well model makes several assumptions, including that the particle is confined within an infinitely deep potential well, there are no external forces acting on the particle, and the walls of the well are perfectly rigid. It also assumes that the particle has no spin and is not affected by any magnetic fields.

## What is the wave function in the infinite 1-D well model?

In the infinite 1-D well model, the wave function describes the probability of finding the particle at a specific position within the well. It is a mathematical representation of the particle's quantum state and can be used to calculate the particle's energy and other properties.

## How does the energy of the particle in the infinite 1-D well model change?

In the infinite 1-D well model, the energy of the particle is quantized, meaning it can only take on certain discrete values. As the particle moves within the well, its energy increases or decreases depending on its position. However, the energy cannot exceed a certain maximum value, known as the energy ground state.

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