A hydrogen atom has energy -1.36 10-19 J, and the electron can be in any one of ten different quantum states. find the spectroscopic notation for this atom. I solved and got the principal quantum number is 4, degeneracy is 10. need help with finding the total orbital angular momentum and the maximum z component of total angular momentum plz, thanks

So principal quantum number is n=4 Total orbital angular momentum is For n=4, 1=0, 1,2,3 L = VI(1+ 1)h L = 1h + 2h + v/6h+ 12h L = (1 + 1.414 + 2.45 + 3.46)h L = 8.324 x 1.054 x 10 -34 L = 8.778 x 10 Js This is the total orbital angular momentum .Maximum z-component of total angular momentum is Ly = mjh Lz = 3 x 1.054 x 10 -34 Lz = 3.162 x 10 Js Explanation: Here maximum value of l is m_1=3