Quantum mechanics problem: hypothetical spin quantum number and its

[wee00x]

So we are doing problems involving potential energy of electrons, wave functions, and all that jazz, but I am utterly lost on how to do this problem... The professor threw it at us, and I am completely lost on how to even begin. Please help me

In a different universe from ours the spin quantum number for the electron is observed to be s= 5/2 instead of 1/2 but all other properties of the electron are the same as in ours.

(a) Describe qualitatively the outcome of a Stern-Gerlach experiment on hydrogen atoms in this
universe.

(b) What are the possible values of sz for the electron in this universe and what are the possible angles that the spin angular momentum can make with the z-axis?

(c) Calculate the value of s^2
for the electron in this universe.

(d) How many elements will be present in the first row of the periodic table in this universe? Why?

 

[jbsteele]

(a) In this universe, the Stern-Gerlach experiment on hydrogen atoms would result in five distinct outcomes instead of two. This is because the spin quantum number for the electron is 5/2 instead of 1/2. Therefore, the magnetic field would split the beam into five different paths, each carrying a different spin orientation. (b) The possible values of sz for the electron in this universe are -5/2, -3/2, -1/2, 1/2, 3/2, and 5/2. The possible angles that the spin angular momentum can make with the z-axis are 0°, 72°, 144°, 216°, 288° and 360°. (c) The value of s^2 for the electron in this universe is 25/4. (d) There would be seven elements present in the first row of the periodic table in this universe. This is because the maximum number of electrons that can occupy the first shell of an atom is seven, and the spin quantum number for the electron is 5/2 instead of 1/2, thus allowing for more electrons to be present in the same shell.