3.Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunctionis(2a.)3/2 /3a.2ao , where a, is the Bohr radius.(a)2-axis?What possible angles might the angular momentum vector L make with the(b)What is the most probable radius (in terms of a,) at which the electron isfound?(c)What is the expectation value of r in this state? Note: xe-"dx = 120.(p)S° x*e-dx = 23.91.What is the probability of finding such an electron between a, and oo? Note:

We have a radial wave function of 2p state in hydrogen atom and we have to answer the following…

Answered: 3. Suppose an electron in a hydrogen…

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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?
Which of the following sets of quantum numbers n, l, and m¡ would be possible for an excited state of hydrogen? (circle yes or no) I. n= 4, 1= 2, mị II. n= 3, 1=2, m¡ = -2 П. п %3D 2, 1%32, т) %3D+1 IV. п %3D17, 1 %3 2, т %3 —2 =-3 Yes/No Yes/No Yes/No Yes/No
3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction e 2ao, where a, is the Bohr radius. 1 is (2ао)3/2 VЗа. (а) What possible angles might the angular momentum vector L make with the Z-axis? (b) What is the most probable radius (in terms of a.) at which the electron is found? (c) What is the expectation value of r in this state? Note: S xe-"dx 120. (d) What is the probability of finding such an electron between a, and ∞? Note: ° x*e-"dx = 23.91.
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