# Which of the following statements about nodes are true?

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1. Which of the following statements are true? (Select all that apply.)

A) An orbital of principal quantum number n has n –1 nodes.

B) The value of ℓ gives the number of planar (angular) nodes.

2. How many nodes of all types does a 3d orbital have?

• Q1)

A: TRUE

The total number of nodes for a given principal quantum number n is (n-1).

B: TRUE

The number of angular nodes is given by the orbital quantum number ℓ.

Note that:

ℓ=0 is s-orbital

ℓ=1 is p-orbital

ℓ=2 is d-orbital

ℓ=3 is f-orbital

Examples:

For s-orbitals, ℓ=0, thus they have ZERO angular nodes (Testifies B)

1s orbital has ZERO nodes (Testifies A, since n-1 = 1 – 1 = 0 total)

2s orbital has ONE radial node (Testifies A, since n-1 = 2 – 1 = 1 total)

3s orbital has TWO radial nodes (Testifies A, since n-1 = 3 – 1 = 2 total)

4s orbital has THREE radial nodes (Testifies A, since n-1 = 4 – 1 = 3 total)

For p-orbitals, ℓ=1, thus they have ONE angular node (Testifies B)

2p orbital has ONE angular node + ZERO radial node (Testifies A, since n-1 = 2 – 1 = 1 total)

3p orbital has ONE angular node + ONE radial node (Testifies A, since n-1 = 3 – 1 = 2 total)

4p orbital has ONE angular node + TWO radial node (Testifies A, since n-1 = 4 – 1 = 3 total)

For d-orbitals, ℓ=2, thus they have TWO angular node (Testifies B)

3d orbital has TWO angular node + ZERO radial node (Testifies A, since n-1 = 3 – 1 = 2 total)

4d orbital has TWO angular node + ONE radial node (Testifies A, since n-1 = 4 – 1 = 3 total)

For f-orbitals, ℓ=3, thus they have THREE angular node (Testifies B)

4f orbital has THREE angular node + ZERO radial node (Testifies A, since n-1 = 4 – 1 = 3 total)

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Q2) From the examples above, we can see that:

3d orbital has TWO angular node + ZERO radial node

Source(s): I teach chemistry

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