For a given value of l, how many values of m are permissible?

Explanation

To determine how many values of \( m \) are permissible for a given value of \( l \), we can follow these steps:

### Step 1: Understand the quantum numbers
In quantum mechanics, the quantum number \( l \) represents the azimuthal quantum number, which describes the shape of the orbital. The magnetic quantum number \( m \) describes the orientation of the orbital in space.

### Step 2: Identify the range of \( m \)
For a given value of \( l \), the permissible values of \( m \) range from \(-l\) to \(+l\). This means that \( m \) can take on any integer value within this range.

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