Question

Describe the shapes and relative energies of the s,p,d, and f atomic orbitals?

Answer 1

Relative energies are in the order:

s < p < d < f

And the shape of these orbitals are

s - spherical

p - dumbbell

d - double dumbbell        

f -   double double dumbbell  

Answer 2

The shapes of s, p, d and f orbitals are spherical, dumbbell, clover leaf and double dumbbell respectively. (For structures, refer to the attached image). The relative energies of these orbitals follows the order $s < p < d < f$.

Further explanation:

Atomic Orbital:

It is a mathematical function required for the description of the wave-nature of electrons in an atom. The probability to find an electron in a specific region around the nucleus of an atom is determined by these orbitals. Four different types of atomic orbitals are present. These are s, p, d and f orbitals. The value of quantum numbers is different for each atomic orbital.

An atom can be occupied by various orbitals. The size of the orbitals is related to the possibility of finding electrons. Smaller the size of orbitals, higher will be the possibility to find electrons and vice-versa.

The s orbitals are nondirectional in nature and therefore have spherical shape. This is because these have spherical symmetry and the wave function depends only on the distance from the nucleus but not on the direction. (For shape, refer to the attached image).

The p orbitals have dumbbell shape. These are of three types, ${p_x}$, ${p_y}$ and ${p_z}$. (For shape, refer to the attached image).

The d orbitals have shape somewhat similar to a clover leaf. These are of five types- ${d_{xy}}$, ${d_{yz}}$, ${d_{xz}}$, ${d_{{x^2} - {y^2}}}$ and ${d_{{z^2}}}$. These orbitals have two angular nodes where the probability of finding electrons is zero. (For shape, refer to the attached image).

The f orbitals have double dumbbell shape. These are of seven types- ${f_{xyz}}$, ${f_{y\left( {{x^2} - {z^2}} \right)}}$, ${f_{z\left( {{x^2} - {y^2}} \right)}}$, ${f_{x\left( {{z^2} - {y^2}} \right)}}$, ${f_{{x^3} - \frac{3}{5}x{r^2}}}$, ${f_{{z^3} - \dfrac{3}{5}z{r^2}}}$  and ${f_{{y^3} - \dfrac{3}{5}y{r^2}}}$. (For shape, refer to the attached image).

The energy of various orbitals depends on the principal quantum number (n) and azimuthal quantum number (l). More the value of n, higher will be the energy and vice-versa. In case, orbitals have the same value of n, that having higher (n + l) will have higher energy. The increasing order of energy of various orbitals is,

$s < p < d < f$  

Learn more:

1. The major contribution of Antoine Lavoisier to chemistry: brainly.com/question/2500879
2. Example of physical change: brainly.com/question/1119909

Answer details:

Grade: High School

Subject: Chemistry

Chapter: Atomic Structure

Keywords: atomic orbital, shape, energy, s, p, d, f, spherical, dumbbell, double dumbbell, clover leaf, nucleus.