Question

If an electron has orbital angular momentum quantum number $l=7,$ then it will have an orbital angular momentum equal to

• A. $7\left(\frac{h}{2\pi }\right)$
• B. $42\left(\frac{h}{2\pi }\right)$
• C. $\sqrt{7}\left(\frac{h}{2\pi }\right)$
• D. $\sqrt{56}\left(\frac{h}{2\pi }\right)$

Answer 1

Answer: (D)

$L=\sqrt{l(l+1)}\frac{n}{2\pi }$
$L=\sqrt{7(7+1)}\frac{h}{2\pi }$
$L=\sqrt{7\times 8}\frac{h}{2\pi }=\sqrt{56}\left(\frac{h}{2\pi }\right)$