Electronic energy of hydrogen atom depends on the quantum number

The electronic energy of a hydrogen atom depends on the quantum numbers that describe its state. The quantum numbers are mathematical values that characterize certain properties of the atom, such as its energy level, orbital shape, and orientation in space. The three main quantum numbers are the principal quantum number (n), the azimuthal quantum number (l), and the magnetic quantum number (m).

a) n, l, and m
The electronic energy of a hydrogen atom depends on all three quantum numbers: n, l, and m.

- The principal quantum number (n) determines the energy level of the electron. It represents the shell or energy level in which the electron resides. The higher the value of n, the higher the energy level and the farther the electron is from the nucleus. The energy of the electron increases with increasing n.

- The azimuthal quantum number (l) determines the shape of the orbital or the subshell in which the electron is located. It can have values ranging from 0 to (n-1). The value of l affects the energy of the electron because different orbital shapes have different energies. For example, s orbitals have lower energy than p orbitals.

- The magnetic quantum number (m) specifies the orientation of the orbital in space. It can have values ranging from -l to +l. The orientation of the orbital affects the energy because different orientations have different spatial distributions and thus different electron densities.

The combination of these three quantum numbers determines the electronic energy of a hydrogen atom. Each set of quantum numbers corresponds to a unique energy level, orbital shape, and orientation. Thus, changing any of these quantum numbers will result in a different electronic energy state for the hydrogen atom.

b) n and l only
If we consider only the quantum numbers n and l, the electronic energy of a hydrogen atom can still be determined to a large extent. The principal quantum number (n) determines the energy level, and the azimuthal quantum number (l) determines the shape of the orbital. These two quantum numbers play a significant role in determining the energy of the electron. However, the magnetic quantum number (m) is also important as it affects the orientation of the orbital in space. Therefore, considering only n and l would provide a partial understanding of the electronic energy of the hydrogen atom.

c) n and m only
Considering only the quantum numbers n and m would provide an incomplete understanding of the electronic energy of a hydrogen atom. While the principal quantum number (n) determines the energy level and the magnetic quantum number (m) determines the orientation of the orbital, the azimuthal quantum number (l) also plays a significant role in determining the energy. The orbital shape, dictated by l, influences the energy of the electron. Thus, considering only n and m would overlook the impact of l on the electronic energy.

d) n only
If we consider only the principal quantum number (n), it gives us information about the energy level of the electron in a hydrogen atom. The higher the value of n, the higher the energy level and the farther the electron is from the nucleus. However, it does not provide information about the shape or orientation of the orbital, which are determined by the azimuthal quantum number (l) and the magnetic quantum number (m) respectively. Therefore, considering only n would not fully describe the

N only