Among the given elements, Cr has the least metallic radii. The CrO$_4^{2-}$ ion has Cr$^{6+}$, which has a $d^0$ configuration (diamagnetic).
The spin-only magnetic moment:
\[\mu = \sqrt{n(n+2)} \, \text{BM},\]
where $n = 0$.
Final Answer:
\[0 \, \text{BM}.\]
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: