Question

Which is higher in energy: the 2s or 2p orbital in hydrogen? Is this also true for helium? Explain

Short answer

In hydrogen, there is no difference in energy between the 2s and 2p orbitals, as their energy levels depend only on the principal quantum number (n). However, for helium, a multi-electron atom, the 2p orbital has higher energy compared to the 2s orbital due to the influence of both the principal (n) and azimuthal (l) quantum numbers.

Step-by-step solution

Understand atomic orbitals and their energy levels

Atomic orbitals represent the regions in space where electrons are most likely to be found. These orbitals have different shapes and orientations and are classified into different types such as s, p, d, and f orbitals. The energy levels of these orbitals are determined by the principal quantum number (n) and the azimuthal quantum number (l). For the hydrogen atom, the energy of an orbital is determined only by the principal quantum number (n). However, for multi-electron atoms like helium, the energy of an orbital is influenced by both principal quantum number (n) and azimuthal quantum number (l). In general, when comparing orbitals with the same n value, those with a higher l value will have higher energy.

Identify electron configurations for hydrogen and helium

Electron configurations can be determined by the periodic table. For hydrogen, its electron configuration is 1s1, meaning it has only one electron in the 1s orbital. For helium, its electron configuration is 1s2, which indicates that it has two electrons in the 1s orbital.

Compare the energy levels of 2s and 2p orbitals in hydrogen

As mentioned earlier, for hydrogen, the energy level of an orbital is determined only by the principal quantum number (n). In this case, both 2s and 2p orbitals have the same n value of 2, so their energies are equal. Therefore, there is no difference in energy between the 2s and 2p orbitals for hydrogen.

Compare the energy levels of 2s and 2p orbitals in helium

For helium, a multi-electron atom, the energy of an orbital is influenced by both principal quantum number (n) and azimuthal quantum number (l). Since the 2s orbital has an l value of 0, while the 2p orbital has an l value of 1, the 2p orbital will have higher energy compared to the 2s orbital in helium.

Explain the comparison

In summary, for hydrogen, there is no difference in energy between the 2s and 2p orbitals, as their energy levels depend only on the principal quantum number (n). However, for helium, the 2p orbital has higher energy due to the influence of both principal (n) and azimuthal (l) quantum numbers.

Key concepts

Energy Levels

Understanding energy levels is crucial in grasping how electrons behave within an atom. Energy levels refer to the fixed distances from an atom's nucleus where electrons can orbit. These levels are often visualized as the steps of a staircase.

• Lower energy levels are closer to the nucleus, meaning electrons there have less energy.
• Higher energy levels are further away, where electrons possess more energy.

In hydrogen atoms, since there is only one electron, the energy level of any orbital is primarily determined by the principal quantum number (n), regardless of the shape or type of the orbital. However, in atoms with more than one electron, like helium, the energy levels of orbitals are affected by both the principal and azimuthal quantum numbers. This is because electron-electron interactions come into play, leading to energy differences even among orbitals with the same principal quantum number.

Electron Configuration

Electron configuration is a method to denote the arrangement of electrons in an atom. This notation employs numbers, letters, and superscripts to convey the distribution of electrons across different orbitals.

• For example, the electron configuration of hydrogen is written as 1s¹, indicating one electron in the 1s orbital.
• Helium, with its two electrons, has a configuration of 1s².

This notation helps us understand the electron's placement and its likely energy level within the atom. The configuration can vary between atoms based on electron count and orbital filling order, a concept defined by the Pauli exclusion principle and Hund's rule. For atoms like helium, the placement of electrons according to azimuthal quantum number influences the overall energy and, consequently, configuration characteristics.

Principal Quantum Number

The principal quantum number, often expressed as 'n', plays a significant role in describing the energy of an electron in an atom. It determines the size and energy of the atomic orbitals.

• Higher values of n correspond to orbitals further from the nucleus and with higher energy.
• The principal quantum number can take integer values starting from 1 upward (1, 2, 3...etc.).

In hydrogen atoms, where the effect of the electron-electron interaction is absent, the energy of an orbital depends solely on this number. Thus, in hydrogen, 2s and 2p orbitals have the same energy because they share the same 'n'. However, when other interactions are considered, especially in multi-electron atoms like helium, different orbitals with the same n may still have differing energy levels.

Azimuthal Quantum Number

The azimuthal quantum number, symbolized as 'l', gives further information about the angular momentum of electron orbitals in atoms. This quantum number determines the shape of the orbital and plays a key role in multielectron atomic systems.

• The values of l range from 0 to n-1, where 'n' is the principal quantum number.
• The shapes associated with l are named s (l=0), p (l=1), d (l=2), and f (l=3), defining the orbital shape complexity.

In helium, for instance, despite the 2s and 2p orbitals having the same principal quantum number, their differing azimuthal quantum numbers result in differing energies between these orbitals. This is due to electron-electron interactions and the preference of electrons for certain energy levels over others, affecting their overall placement and behavior in atoms. Thus, the azimuthal quantum number is essential in distinguishing between orbitals, especially in multi-electron environments.