8.8 Calculate by direct integration the expectation values (r) and (1/r) of the radial position forthe ground state of hydrogen. Compare your results to the quoted expressions in Eq. (8.89)and discuss your results. Did you expect that (1/r) # 1/(r)? Use your result for (1/r) tofind the expectation value of the kinetic energy of the ground state of hydrogen and discussyour result.8.9 Calculate by direct integration the expectation value of the radial position for each of the

Answered: Image /qna-images/answer/12bd5eba-2836-444d-8819-21ac0451e9cc.jpg

Answered: 8.8 Calculate by direct integration the…

Similar questions

Ignoring the fine structure splitting, hyperfine structure splitting, etc., such that energy levels depend only on the principal quantum number n, how many distinct states of singly-ionized helium (Z = 2) have energy E= -13.6 eV? Write out all the quantum numbers (n, l, me, ms) describing each distinct state. (Recall that the ground state energy of hydrogen is E₁ = -13.6 eV, and singly-ionized helium may be treated as a hydrogen-like atom.)
In the following questions, we will use quantum states made up of the hydrogen energy eigenstates: Q1: Consider the election in a hydrogen atom to initially be in the state: F A. B. C. a) What is the probability of measuring the energy of this state and obtaining E₂? √3 √ vnim (r0,0)=R(r)Y," (0,0) always Y(t = 0) = √3 R₁OYO at t=0 but something different at t>0 ² at t=0 but something different at t>0 D. always 3 + E. Something else. b) Explain your answer. R₂₁ + R32Y₂¹
could you also explain to me how you come up with question A?
Problem 4.25 If electron, radius [4.138] 4πεmc2 What would be the velocity of a point on the "equator" in m /s if it were a classical solid sphere with a given angular momentum of (1/2) h? (The classical electron radius, re, is obtained by assuming that the mass of the electron can be attributed to the energy stored in its electric field with the help of Einstein's formula E = mc2). Does this model make sense? (In fact, the experimentally determined radius of the electron is much smaller than re, making this problem worse).
Write down the partition function for this system. What's the probability of finding the atom in its ground state, if e/kT = In (3)? Assume now that the atom has a second excited state that's 9-fold degenerate and has energy 26. What's the probability of finding the atom with energy E = 2ɛ, again
An electron is confined to a 1-dimensional infinite potential well of dimensions 1.55 nm. Find the energy of the ground state of the electron. Give your answer in units of electron volts (eV). Round your answer to 2 decimal places. Add your answer