Define energy level and orbital. State the shape of s and p orbitals. How many electrons can be held in one s, one p, and a full set of p orbitals? How many orbitals are in the first and second energy

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1. Basic Concepts

a) Define the following terms:

i) Energy level: A principal energy level (or shell) is a region around the nucleus of an atom where electrons are likely to be found, characterized by a specific principal quantum number ($n$). Electrons in higher energy levels are further from the nucleus and have higher energy.

ii) Orbital: An atomic orbital is a mathematical function that describes the wave-like behavior of an electron or a pair of electrons in an atom. It defines a region within an energy level where there is a high probability of finding an electron.

b) State:

i) Shape of an s orbital: Spherical

ii) Shape of a p orbital: Dumbbell-shaped

c) How many electrons can be held in:

i) One s orbital: $\boxed{\text{2 electrons}}$

ii) One p orbital: $\boxed{\text{2 electrons}}$

iii) A full set of p orbitals: A full set of p orbitals consists of three p orbitals ($p_x, p_y, p_z$). Each can hold 2 electrons.

$$3 \text{ orbitals} \times 2 \text{ electrons/orbital} = 6 \text{ electrons}$$

$\boxed{\text{6 electrons}}$

2. Structure Understanding

a) How many orbitals are found in:

i) First energy level: The first energy level ($n=1$) contains only one s orbital (1s).
$\boxed{\text{1 orbital}}$

ii) Second energy level: The second energy level ($n=2$) contains one s orbital (2s) and three p orbitals ($2p_x, 2p_y, 2p_z$).

$$1 \text{ (s orbital)} + 3 \text{ (p orbitals)} = 4 \text{ orbitals}$$

$\boxed{\text{4 orbitals}}$

b) Explain why the first energy level has no p orbitals:
The first energy level ($n=1$) only has one subshell, which is the s subshell. The p subshell only becomes available starting from the second energy level ($n=2$). This is determined by the allowed values of the azimuthal quantum number ($l$), where $l$ can range from 0 to $n-1$. For $n=1$, $l$ can only be 0, which corresponds to an s orbital.