Particle (infinite 1-D well)

[mss90]

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?

 

[ZetaOfThree]

You need to attempt the problem before we will help.

 

[mss90]

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

 

[mss90]

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

 

[HalfLostAndSearching]

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.