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

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To determine the energy needed to transition a particle from the ground state (n=1) to the third excited state (n=4) in an infinite 1-D well, the relevant equations are En = n²π²ħ²/(2mL²) and En = h²k²n²/(2m). The initial energy for n=1 is given as 1.26 eV. The calculations involve substituting the values for mass and Planck's constant to find the energy levels for n=4. The discussion emphasizes the need for initial attempts at solving the problem before seeking further assistance.
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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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Im thinking En = h2kn2/(2m) or En = n2π2ħ2/(2mL2)?
 
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
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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