Determine the mean radius for the 2s electron.

▼ Part A For an electron in the 1s state of hydrogen, what is the probability of being in a spherical shell of thickness 1.00×10-2 ap at distance aB? ▸ View Available Hint(s) 15. ΑΣΦ ? Part B For an electron in the 1s state of hydrogen, what is the probability of being in a spherical shell of thickness 1.00×10-2 ag at distance ag from the proton? ▸ View Available Hint(s) [5] ΑΣΦ ? Submit Submit

In high static-magnetic field environment, such stellar interiors, the energy levels of a H-atom are modified in such a way that they depend on l and m in addition to n. In this problem assume that the eigenvectors of Ĥo, β and Î₂ are still the usual In, l, m), but the energy is eigenvalue is Enem O Ĥ Φ nem (r,0,0) = EnemÞµlm (1,0,0) 13.6eV ■ E 'nlm = +0.1m 1+ n 。 Znm (1,0,0) = l (l+1)ħ²Þntm (r,0,0) O Î₂nem (r,0,0) = mħÞ, Dnem (1,0,0) 1 2l+1 Consider the n = 2 level. Calculate the energy eigenvalues for all 4 states. Draw a stack of lines in order of increasing energy with the lowest one at the bottom

Derive the rn, vn and En the quantized parameters for a hydrogen-like atom with a number of protons that you will keep in your derivation of the answers as Z. Note:1) An example of the situation would for instance He+ with one single electron left to orbit the nucleus of Helium or Li++ with one single electron left to orbit the nucleus of Lithium.

.8 O An electron is trapped in a one-dimensional infinite well and is in its first excited state. Figure 39-27 indicates the five longest wavelengths of light that the electron could absorb in transitions from this initial state via a single photon absorption: A, = 80.78 nm, A, = 33.66 nm, A = 19.23 nm, A, = 12.62 nm, and A, = 8.98 nm. What is the width of the potential well? %3D %3! 2 (nm) Figure 39-27 Problem 8.

Consider the values of s and ms for an electron.   Write all possible values of s for an electron.

Compute the intrinsic line-width (AX) of the Lyman a line (corresponding to the n = 2 to n = 1) transition for the Hydrogen atom. You may assume that the electron remains in the excited state for a time of the order of 10 s. The line-width may be computed using: e hc ΔΕ

You have the energy matrix for only 4x4 elements. Calculate the expected value of energy (E) using the function 1 1 -fox /2 e -3icut 2 [e heo S 0 0 0 2 E= = 5 0 0 e 0 2 0 0 0 Ther 2 J Al Laxities (E) A8l 2 gidd) dasll Cuaal l o |2 l Jiew /2 Vi *[fi“ e 0:‘ 5

a)  Calculate the energy of the emissive transition with the lowest energy possible for the Lyman series, for a mole of hydrogen atoms. Express your answer in joules/mol. b) Is this transition in the visible spectral domain? If not, in which region is it located?