Statement 1: The free gaseous chromium atom has six unpaired electrons.

Statement 2: Half-filled orbital has greater stability than fully filled.

Statement 1: True, Electron configuration of Cr(g) is ${\left[\mathrm{Ar}\right]}^{18}3{\mathrm{d}}^{5}4{\mathrm{s}}^1$ and, therefore, it has six unpaired electrons.

Statement 2: False, Fully filled orbital is more stable than half filled orbital on account of more number of exchange of electrons resulting into the greater release of exchange energy.