We are given that:
1 atom N = 3 atom of the metal
1 mol N = 3 mol of the metal
First let us convert the given nitrogen into number of moles:
moles N = 1 g / (14 g / mol)
moles N = 0.071 mol
Therefore the atomic or molar mass of the metal is:
molar mass = 1.486 g / (3 * 0.071 mol)
molar mass = 6.93 g / mol