Chemistry Q63 – NEET-UG 2023

Home Chemistry Structure of AtomQuestion #614

The relation between

n_{m}

, (

n_{m}

= the number of permissible values of magnetic quantum number (

m

)) for a given value of azimuthal quantum number (

l

), is

Clue 1 of 3: Quantum Numbers

Recall the definitions and allowed values for azimuthal and magnetic quantum numbers.

🥷

Ninja Strategy•Test with Simple Values

By testing the simplest case ( $l = 0$ ), options (2) and (4) can be quickly eliminated, narrowing down the choices to (1) and (3).

🧠 Full Solution Path

Step 1: Recall the relationship between

l

and

m

✦ Active

For a given azimuthal quantum number ( $l$ ), the magnetic quantum number ( $m$ ) can take integer values from $- l$ to $+ l$ , including $0$ . These values are: $- l, - (l - 1), \dots, - 1, 0, 1, \dots, (l - 1), l$ .

Step 2: Calculate the number of permissible values of

m

○ Expand

The total number of permissible values of $m$ , denoted as $n_{m}$ , is given by the formula:

n_{m} = (l) - (- l) + 1 = l + l + 1 = 2 l + 1

💡 Teacher's Secret Hint

Remember that the count includes zero and both positive and negative integers.

Step 3: Match with the given options○ Expand

We have the relation $n_{m} = 2 l + 1$ . Let's rearrange this to match the options:

n_{m} - 1 = 2 l

l = \frac{n_{m} - 1}{2}

This matches option (1).

💡 Teacher's Secret Hint

Always check if the derived formula can be rearranged to match one of the options.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Chemistry Question 63 – NEET-UG 2023

Clue 1 of 3: Quantum Numbers

🧠 Full Solution Path