What is the lowest rotational energy level for a diatomic molecule?

In summary, The rotational quantum number of 0 indicates that an electron is not rotating around the nucleus and therefore has no angular momentum. This results in an s orbital with the lowest energy level in an atom. The maximum value for this quantum number is 0, representing the ground state of an atom. An electron with a rotational quantum number of 0 has a symmetrical orbital shape with no distinct orientation in space. This is true for all types of atoms, though the orbital shapes and energy levels may vary.
  • #1
spaghetti3451
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My book on Physics by Beiser specifies that the rotational energy levels of a diatomic molecule are given by J(J+1)/ℏ2, where J = 0, 1, 2, 3, ... .

However, in the next page, it goes on to mention that the lowest rotational energy level corresponds to J = 1.

I don't see why that shouldn't be J = 0.

Any comments would be greatly appreciated.
 
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  • #2
Let me rephrase my question.

I know that the rotational quantum number starts at J = 0,

but do you count the lowest rotational energy state as J = 0 or as J = 1?
 
  • #3
J = 0 is the ground state. J = 1 is the first excited rotational state.
 
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1. What is the significance of having a rotational quantum number of 0?

The rotational quantum number, also known as the angular momentum quantum number, indicates the amount of angular momentum that an electron carries as it rotates around the nucleus of an atom. A value of 0 for this quantum number means that the electron is not rotating around the nucleus and therefore has no angular momentum. This is known as an s orbital, where the electron is in a spherical shape around the nucleus.

2. How does a rotational quantum number of 0 affect the energy level of an electron?

Electrons with a rotational quantum number of 0 have the lowest energy level in an atom. This is because they are not moving and therefore do not possess any kinetic energy. They are also closer to the nucleus, which results in a lower potential energy. As the rotational quantum number increases, the energy level of the electron also increases.

3. What is the maximum value for the rotational quantum number 0?

The maximum value for the rotational quantum number 0 is 0. This means that an electron can only have an s orbital and cannot rotate around the nucleus. This is also known as the ground state of an atom.

4. How does a rotational quantum number of 0 affect the shape of an electron's orbital?

Since an electron with a rotational quantum number of 0 is in a spherical shape, it does not have any angular momentum or rotation. This results in a symmetrical orbital shape with no distinct orientation in space. As the rotational quantum number increases, the shape of the orbital becomes more complex and can have different orientations in space.

5. Can an electron have a rotational quantum number of 0 in any type of atom?

Yes, an electron can have a rotational quantum number of 0 in any type of atom. The orbital shapes and energy levels may vary between different types of atoms, but the concept of having a rotational quantum number of 0 remains the same. However, in some atoms, such as hydrogen, the s orbital is the only possible orbital for an electron with a rotational quantum number of 0.

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