The magnitude of an orbital angular momentum vector of an electron is $\sqrt{6}\frac{h}{2\pi }.$ Into how many components will the vector split if an external field is applied to it?

The orbital angular momentum is given by $\sqrt{l(l+1)}\times h/2\pi$

In the question, it is given to be $\sqrt{6}\times h/2\pi$

So, it means $\sqrt{l(l+1)}=\sqrt{6}$

$l=2$

The possible values of magnetic quantum numbers for $l=2$ will be $m_l=-2,-1,0,1,2$

So, the vector can split into FIVE components in the presence of the external magnetic field