An electron is contained in a one-dimensional box of length 0.100 nm. Calculate the energy of the electron in the 3rd state.
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- 3. Particle in a 2D Box. A quantum mechanical particle is confined in side a square 2D box, with side length L. Inside the box V=0 and outside the box V=infinity. Let the wave function to be (x,y). (a) write down the Schrodinger equation of (x,y). (b) Use the separation of variable method solve (x,y) (let the quantum numbers to be nx and ny.) (c) What is the energy for the state (nx, ny)? (d) What is the probability density p(x,y) for the state nx=3 and ny=3? Sketch this p(x,y) in a square.7. One electron is trapped in a one-dimensional square well potential with infinitely high sides. a. If you have a probe that has a width for electron detection Ax = 0.00350L in the x direction, for the first excited state ( n =2), what is the probability that the electron is found in the probe when it is centered at x = L/4, (hint: you can use an approximation for this - you do not need to do an integral)? b. What is the average number of electrons that you would detect using the probe described in part "b." centered at x = L/4, ifthe electron is in the first excited state (n = 2) for each experiment and you repeat the experiment N, =100,000 times?The lifetimes of the levels in a hydrogen atom are of the order of 10-8 s. Find the energy uncertainty of the first excited state and compare it with the energy of the state. 3 p RO
- An electron is trapped inside a 1.00 nm potential well. Find the wavelength of the photons when the electron makes a transition from n =4 to n= 1.The kinetic energy operator in 3-D is: a. Î= – Invalid element O b. O C. O d. T= ħ2² 2m - ·D2 ħ 2m ħ 2m V VA Proton is confined to move in a one- dimensional bux of length 0.410 m a) Find the lowest possible energy of the proton. Note: Answer must be in ev