Consider the 5p orbital of a hydrogen atom.

1. how many different 5p orbitals are there?
2. how many radial nodes are there?
3. how many angular nodes are there? (i.e. how many nodal planes or surfaces, not including radial nodes)

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To answer these questions, let's first understand the characteristics of the 5p orbital of a hydrogen atom.

1. The 5p orbital is one of the orbitals in the shell with the principal quantum number n = 5 and the angular momentum quantum number l = 1. According to the quantum mechanical model, each combination of n and l gives rise to a specific orbital. The magnetic quantum number (ml) can take values ranging from -l to +l, including zero. Therefore, for the 5p orbital, there are three different 5p orbitals: one for ml = -1, one for ml = 0, and one for ml = +1. These three orbitals have different orientations in space.

2. Radial nodes are regions of zero electron density located along the radial direction from the nucleus. The number of radial nodes can be determined using the formula: (n - l - 1), where n is the principal quantum number and l is the angular momentum quantum number. For the 5p orbital (n = 5, l = 1), there are (5 - 1 - 1) = 3 radial nodes.

3. Angular nodes, also known as nodal planes or surfaces, represent regions in space where the probability of finding an electron is zero. For the 5p orbital, there is one angular node. This node corresponds to the equatorial plane passing through the nucleus. It divides the orbital into two equal lobes above and below the plane.

In summary:
1. There are three different 5p orbitals for ml = -1, ml = 0, and ml = +1.
2. There are three radial nodes.
3. There is one angular node.