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Lecture Note - Orbital Shape

# Lecture Note - Orbital Shape - 1s electron 2p-orbital When...

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Electron Orbital Shapes Now, let's look closer at these electron orbitals and their shapes. Remember, we used a two- dimensional plot of the wave function versus x to visualize the standing wave of an electron trapped in one dimension. To visualize the standing waves (or orbitals) of electrons bound to a positively charged nucleus in three dimensions, we will need a four-dimensional plot of the wave function vs. x, y, and z. This can be a bit tricky since our visual perception is limited to three spatial dimensions. So we will need a few tricks to help us visualize the four-dimensional standing waves of the electron in 3 dimension. 1s-orbital: The lowest energy orbital of the hydrogen atom. 2s-orbital: The second harmonic state.

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Remember that at the node, the probability of finding the electron is zero. In general, an orbital with high n (principal quantum number) (e.g. n = 2, 3, 4. ..) means that the electron will extend out from the nucleus further, and so will be held less tightly than a

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Unformatted text preview: 1s electron. 2p-orbital: When n = 2, we have 2 possible values for ℓ. The first is ℓ = 0, or 2s orbital, which we just discussed above. The second possibility is ℓ = 1 or the 2 p orbital. For a given value of ℓ there are 2 ℓ + 1 possible m l values. So for ℓ = 1, we have m ℓ = -1, 0, +1. These three values of m ℓ correspond to three different p-orbitals. P-orbitals look like dumbbells along each axis. Instead of a radial node, we have an angular node, which lies along the plane perpendicular to the axis in which the orbital lies. Since the energy, E, of each orbital is a function of only n, then all the n = 2 orbitals (2s, 2p x , 2p y , 2p z ) have the same energy. n = 3 orbitals: For the n=3 orbitals the possible quantum numbers are: n=3 ℓ=0 m ℓ =0 3s orbital n=3 ℓ=1 m ℓ =-1, 0, +1 3p orbitals n=3 ℓ=2 m ℓ =-2, -1, 0, +1, +2 3d orbitals For much nicer three-dimensional renderings of all the atomic orbitals visit Mark Winter's Orbitron site ....
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Lecture Note - Orbital Shape - 1s electron 2p-orbital When...

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