Chapter 7: Problem 56

Give the values of the four quantum numbers of an electron in the following orbitals: (a) \(3 s,\) (b) \(4 p,\) (c) \(3 d\).

Short Answer

Expert verified

Four quantum numbers for an electron in (a) 3s are n=3, l=0, m=0, and s=+1/2. For (b) 4p, the numbers are n=4, l=1, m=0, and s=+1/2. And for (c) 3d, they are n=3, l=2, m=0, and s=+1/2.

Step by step solution

Determining the Principal Quantum Number (n)

The first digit in the orbital notation represents the principal quantum number. So for (a) 3s, n is 3, for (b) 4p, n is 4 and for (c) 3d, n is 3.

Determining the Azimuthal Quantum Number (l)

The lette r(s, p, d, f etc.) in the orbital notation represents the azimuthal quantum. Here, s corresponds to l = 0, p to l = 1, d to l = 2, and so on. Hence, for (a) 3s, l = 0, for (b) 4p, l = 1 and for (c) 3d, l = 2.

Determining the Magnetic Quantum Number (ml)

The magnetic quantum number can have any integral value between -l and +l. As a simplified example, let's assume that the electron is in the most 'average' state, so, its ml value would be 0. Thus, for (a) 3s where l=0, ml is 0. For (b) 4p where l=1, ml can be any value between -1 and +1, so we'll also assume ml = 0 here. Finally, for (c) 3d where l=2, ml could range from -2 to +2, for simplicity, we'll again consider ml = 0.

Determining the Spin Quantum Number (s)

The spin quantum number, s, can be either +1/2 or -1/2. Let's assume that the spin of the electrons are +1/2 in all cases because all electrons are identical and the choice of +1/2 or -1/2 is arbitrary.

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Give the values of the four quantum numbers of an electron in the following orbitals: (a) \(3 s,\) (b) \(4 p,\) (c) \(3 d\).

Short Answer

Step by step solution

Determining the Principal Quantum Number (n)

Determining the Azimuthal Quantum Number (l)

Determining the Magnetic Quantum Number (ml)

Determining the Spin Quantum Number (s)

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