Questions: Which orbital is described by the quantum numbers n = 3, 1 = 1? Please write a step by step guide onhow to Make a sketch of this orbital.

Solution Steps

• The principal quantum number \( n = 3 \) indicates the third energy level.
• The azimuthal quantum number \( l = 1 \) corresponds to a \( p \)-orbital.
• Therefore, the orbital described is a \( 3p \)-orbital.

• \( p \)-orbitals have a dumbbell shape.
• They consist of two lobes on either side of the nucleus, with a node at the nucleus where the probability of finding an electron is zero.

• \( p \)-orbitals can be oriented along the x, y, or z-axis, known as \( p_x \), \( p_y \), and \( p_z \).
• Without additional information, any of these orientations can be chosen for the sketch.

• Draw two lobes along the chosen axis (e.g., the z-axis for a \( p_z \)-orbital).
• Ensure the lobes are symmetrical about the nucleus.
• Indicate the node at the nucleus where the lobes meet.

• Label the axis along which the orbital is oriented.
• Indicate the node at the center.
• Optionally, label the lobes as positive and negative to represent the phase of the wave function.

Final Answer