CSIR NET 2020 June — Angular momentum in Atomic Physics previous year question

If we take the nuclear spin I into account, the total angular momentum is $\overrightarrow{\mathrm{F}}=\overrightarrow{\mathrm{L}}+\overrightarrow{\mathrm{S}}+\overrightarrow{\mathrm{I}}$, where $\overrightarrow{\mathrm{L}}$ and $\overrightarrow{\mathrm{S}}$ are the orbital and spin angular momenta of the electron. The Hamiltonian of the hydrogen atom is corrected by the additional interaction $\lambda \overrightarrow{\mathrm{I}}\cdot (\overrightarrow{\mathrm{L}}+\overrightarrow{\mathrm{S}})$, where $\lambda >0$ is a constant. The total angular momentum quantum number F of the p - orbital state with the lowest energy is