Help me understand these questions with explanations and answers. Schrondingers

Question

Help me understand these questions with explanations and answers.

Schrondingers cat (Bohr) is messing with the wave function. All of a sudden, the rules of the quantum mechanics have changed.

Change 1: Bohr changed the universe so that m sub s can have three values: +1/2, 0, -1/2. Determine how may electrons can be in the 4th shell and how many electrons are in the subshell l=4.

Change 2: The universe is back to its normal self (m sub s = +1/2 and -1/2) but then Bohr changed the universe so that m sub l can only have positive values or be zero. Determing how many electrons can be in the 4th shell and how many electrons are in the subshell with l=4.

Explanation / Answer

l = 4 can have ml = -4 to +4 total 2l+1 values = 2( 4)+1 = 9 values

each orbit ml has 3 electrons due to three spins +1/2, 0 , -1/2

hence total electrons = 9 x 3 = 27

change 2) l = 4 can have ml = 0 , 1, 2, 3, 4 total 5 values.

each ml can have 2 electrons since two spins , hence total electrons for l = 4 are 10   ( ml = 5)

now shell number n = 4 , ml values = n^2 4^2 = 16

total electrons = 2 x ml = 2 x 16 = 32

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