Question

The angle made by angular momentum vector of an electron with Z-axis is-

• A. cosq = l / m
• B. cosq = $\sqrt{\frac{\mathcal{l}}{m}}$
• C. cosq = $\frac{\sqrt{\mathcal{(l +}1)}\mathcal{l}}{m}$
• D. cosq= $\frac{m}{\sqrt{(\mathcal{l} + 1)}\mathcal{l}}$

Answer 1

Answer: (D)

cosq= $\frac{m}{\sqrt{(\mathcal{l} + 1)}\mathcal{l}}$

Answer 2

Z component of the angular momentum

L_Z = $\frac{mh}{2\pi}$

L_Z = L cos q = $\sqrt{\mathcal{l(l +}1)}$cos q $\frac{h}{2\pi}$

\ $\sqrt{\mathcal{l}(\mathcal{l} + 1)}$ cos q = m

or cos q = $\frac{m}{\sqrt{\mathcal{l}(\mathcal{l} + 1)}}$