Hydrogen Atom and Hydrogen Molecule The observed wavelengths in the line spectrum of hydrogen atom were first expressed in terms of a series by johann Jakob Balmer, a Swiss teacher. Balmer's empirical empirical formula is 1/lambda=R_(H)(1/2^(2)-1/n^(2)),"" N=3, 4, 5 R_(H)=(Me e^(4))/(8 epsilon_(0)^(2)h^(3) c)=109. 678 cm^(-1) Here, R_(H) is the Rydberg Constant, m_(e) is the mass of electron. Niels Bohr derived this expression theoretically in 1913. The formula is easily generalized to any one electron atom//ion. Consider a spherical shell of radius a_(0) and thickness 0.001 a_(0). Estimate the probability of finding the electron in this shell. Volume of a spherical shell of inner radius r and small thickness Deltar equals 4pir_(2) Deltar. The H_(2) molecule can dissociate through two different channels: (i) H_(2) rarr H+H (two separate hydrogen atoms) (ii) H_(2) rarr H^(+)+H^(-) (a proton and a hydride ion) The graph of energy (E) vs internuclear distance (R) for H_(2) is shown schematically in the figure. The atomic and molecular energies are given in the same scale.