The energies of the first ten atoms in the periodic table are calculated with a set of new variational wave functions. The form of the wave functions used is as follows: 1s:ψ1(r)=N1e-μαr[1+(μbr)2], 2s:ψ2(r)=N2[(μr)e-μr-Ne-μcr], 2p:ψ3(r)=N3(μdr)cosθe-μdr, ψ4(r)=N4(μdr)sinθeiφ-μdr, ψ5(r)=N5(μdr)sinθe-iφ-μdr. There are five parameters in all, two for the ls function, two for the 2s and one for the 2p functions. The parameter μ is a scale factor, the best value of which can be determined analytically, leaving but four parameters to be determined numerically. N1,N2,N3,N4 and N5 are normalization factors. The constant N is fixed so that ψ2 is orthogonal to ψ1. The energies and the parameters of the various states are determined by the variational method. The results of this calculation are better than that calculated by Morse, Young and Haurwitz with their wave functions containing four parameters. If we put c=1 in our wave functions, then there are four parameters only in all and it will be found that the results are still better than that found by Morse et al.