Find the expectation value of the radial position for the electron of the hydrogen atom in the 2s and 2p states.
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Find the expectation value of the radial position for the electron of the hydrogen atom in the 2s and 2p states.
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- Schematic of the n=3 → n=2 transitions that may occur when a hydrogen atom is placed in a magnetic field B. Ignore the effect of electron spin.If we neglect interaction between electrons, the ground state energy of the helium atom is E =2 z2((- e2)/(2ao)) = -108.848eV (Z=2). The true (measured) value is – 79.006eV.Calculate the interaction energy e2/r12 supposing that both electrons are in the 1s state and r12 that the spin wave function is anti-symmetric. What E is the ground state energy?For a ground state Cd atom (Z = 48), how many electrons in total have an angular quantum number ℓ = 0 ?
- Answer the following. (a) Write out the electronic configuration of the ground state for nitrogen (Z = 7). 1s22s22p11s22s22p2 1s22s22p31s22s22p41s22s22p51s22s22p6 (b) Write out the values for the set of quantum numbers n, ℓ, m, and ms for each of the electrons in nitrogen. (In cases where there are more than one value, enter the positive value first. Enter positive values without a '+' sign in front of them. Include all possible values.) 1s states n = ℓ = m = ms = ms = 2s states n = ℓ = m = ms = ms = 2p states n = ℓ = m = ms = ms = m = ms = ms = m = ms = ms =The wave function for hydrogen in the 1s state may be expressed as Psi(r) = Ae−r/a0, where A = 1/sqrt(pi*a03) Determine the probability for locating the electron between r = 0 and r = a0.Consider a two-electron spin system in a singlet state. a. If a measurement of one of the electrons shows that it is in a state with sz = 1/2, what is the probability of obtaining another state with sz= +1/2? b. If a measurement of one of the electrons shows that it is in a state with sx = 1/2, what is the probability of obtaining another state with sy = +1/2?