A hydrogen atom is in the state \(|\psi\rangle=\sqrt{\frac{8}{21}}\left|\psi_{200}\right\rangle+\sqrt{\frac{3}{7}}\left|\psi_{210}\right\rangle+\sqrt{\frac{4}{21}}\left|\psi_{311}\right\rangle\) where \(\left|\psi_{\mathrm{nlm}}\right\rangle\) are normalised eigenstates. If \(\hat{L}^2\) is measured in this state, the probability of obtaining the value \(2 \hbar^2\) is
1
\(\frac{13}{21}\)
2
\(\frac{4}{21}\)
3
\(\frac{17}{21}\)
4
\(\frac{3}{7}\)