Why are s-orbital spherically symmetric?

[scariari]

these are some review questions for an exam:


1.why are s-orbital spherically symmetric?

2.What is the probability of finding an electron at or very near to the nucleus? (1s, 2s, 2p...

3.Why does the curve for 1s go to zero for r-> 0? (the curve of the probability density associated with the radial parts of the hydrogen atomic wave functions)

4.Why do we denote p-orbitals by px, py, and pz?

5.How many nodal planes do 1s,2s,3s.. orbitals have?
What about 2p,3p... orbitals?
And finally, 3d...orbitals?

 

[Jhero]

Hello,

Thank you for sharing these review questions for an exam. I would like to provide some explanations and clarifications for these questions.

1. S-orbitals are spherically symmetric because they have a spherical shape, meaning that the electron has an equal probability of being found in all directions around the nucleus. This is due to the fact that s-orbitals have no angular momentum, so the electron's motion is not restricted to a specific direction.

2. The probability of finding an electron at or very near to the nucleus depends on the energy level and the type of orbital. For example, the probability of finding an electron at the nucleus is highest for the 1s orbital, followed by the 2s and 2p orbitals.

3. The curve for the 1s orbital goes to zero for r->0 because it represents the probability density of finding an electron at a particular distance from the nucleus. As the distance approaches zero, the probability of finding the electron also approaches zero. This is due to the Heisenberg uncertainty principle, which states that the position and momentum of a particle cannot be known simultaneously.

4. P-orbitals are denoted by px, py, and pz because they have different orientations in space. The px orbital is aligned along the x-axis, the py orbital is aligned along the y-axis, and the pz orbital is aligned along the z-axis.

5. The number of nodal planes in an orbital depends on its energy level and type. 1s, 2s, and 3s orbitals have no nodal planes, while 2p and 3p orbitals have one nodal plane. 3d orbitals have two nodal planes. Nodal planes are regions in the orbital where the probability of finding the electron is zero.

I hope this helps to clarify these concepts and prepare you for your exam. Good luck!

 

[M98Ranger]

1. S-orbitals are spherically symmetric because the electron probability distribution is the same in all directions around the nucleus. This is due to the fact that the s-orbital has no angular nodes, meaning that the electron cloud is evenly distributed around the nucleus. This results in a spherical shape for the orbital.

2. The probability of finding an electron at or very near to the nucleus is highest for the 1s orbital, followed by the 2s and then the 2p orbitals. The probability decreases as the distance from the nucleus increases.

3. The curve for 1s goes to zero for r-> 0 because of the Heisenberg uncertainty principle. As the electron gets closer to the nucleus, the uncertainty in its position increases, making it less likely to be found near the nucleus.

4. P-orbitals are denoted by px, py, and pz because they have different orientations in space. Px is oriented along the x-axis, py is oriented along the y-axis, and pz is oriented along the z-axis.

5. The 1s orbital has 0 nodal planes, the 2s orbital has 1 nodal plane, and the 3s orbital has 2 nodal planes. The 2p orbitals have 1 nodal plane each, and the 3p orbitals have 2 nodal planes each. The 3d orbitals have 2 nodal planes each. Nodal planes are surfaces where the probability of finding an electron is zero.