Question

Give the value of the quantum number ℓ, if one exists, for a hydrogen atom whose orbital angular momentum has a magnitude of 6√(h/2π).

Answer 1

Answer:

For this angular momentum, no quantum number exist

Explanation:

From the question we are told that

   The magnitude of the angular momentum is  $L = 6\sqrt{\frac{h}{2 \pi} }$

The generally formula for Orbital angular momentum is mathematically represented as

           $L = \sqrt{(l * (l + 1)) } * \frac{h}{2 \pi}$

Where $l$ is the quantum number

now  

We can look at the given angular momentum in this form as

      $L = 6\sqrt{\frac{h}{2 \pi} } = \sqrt{36} * \sqrt{\frac{h}{2 \pi}} }$

comparing this equation to the generally equation for Orbital angular momentum

     We see that there is no quantum number that would satisfy this equation