In the context of the quantum mechanical model of atoms, the values of the quantum numbers $n$ and $l$ for the $2p$ orbital are as follows:

1. Principal Quantum Number ($n$): $n = 2$
   This quantum number specifies the energy level or shell of the electron. For a $2p$ orbital, the principal quantum number is $2$.

2. Azimuthal Quantum Number ($l$): $l = 1$
   This quantum number defines the shape of the orbital. For $p$-orbitals, $l$ is always $1$.

Explanation

• The principal quantum number $n$ indicates the size and energy of the orbital.
• The azimuthal quantum number $l$ can take integer values from $0$ to $n-1$.
  For $n = 2$, $l$ can be $0$ (indicating an $s$-orbital) or $1$ (indicating a $p$-orbital).

Summary for $2p$ Orbital:

• $n = 2$
• $l = 1$

Let me know if you'd like further clarification or details!

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Here are 5 questions related to this topic for further exploration:

1. What are the possible values of $l$ for an orbital with $n = 3$?
2. How are $m_l$ (magnetic quantum number) values determined for a given $l$?
3. What does the magnetic quantum number $m_l$ represent for $2p$ orbitals?
4. Can the spin quantum number $m_s$ be the same for two electrons in the same orbital?
5. Why does the $p$-orbital have a dumbbell shape, and how is it related to $l$?

Tip: Remember that $l$ determines the shape of orbitals, but the number of orientations depends on $m_l$, which ranges from $-l$ to $+l$.