For deuterium  12H or 12D, the value of Rydberg constant is 109707 cm-. (This value reflects a refinement of simple Bohr theory, wherein the orbital radii and Rydberg constant do not depend on electron mass but on the so called reduced mass. The latter mass, in turn, varies slightly with the mass of the nucleus). Find the shortest wavelength in the absorption spectrum of deuterium

(i) R for H 12 = 109707 cm- The shortest wavelength transition corresponds to highest frequency and hence to the highest energy ( ∵E = hu). So, the transitionwill be from ground state (lowest energy state) for which n = 1 to the highest state for which n =∞.Hence,      u¯=RZ21n12−1n22cm−                  =109707×12112−1(∞)2cm−or          1λ=109707(1−0)cm−=109707cm−∴ λ=1109707cm−=9.1152×10−6cm=9.1152×10−6cm×107nm1cmor                 λ=91.152 nm    Ans.