Answer:Step 1: Calculate the frequency of the convergence limit, converting wavelength into m (nm to m = × 10−9) c = ν λ ν = c ÷ λ ν = 3.00 × 108 ÷ 91.16 × 10−9 ν = 3.29 × 1015 s−1Step 2: Substitute into the equation to calculate IE1 for one atom of hydrogen in J mol−1ΔE = h ν IE1 = 6.63 × 10−34 × 3.29 × 1015 IE1 = 2.18 × 10-18 J atom−1Step 3: Calculate IE1 for 1 mole of hydrogen atoms IE1 = 2.18 × 10−18 × 6.02 × 1023 IE1 = 1 313 491 J mol−1Step 4: Convert J mol−1to kJ mol−1 IE1 = 1313 kJ mol−1So the first ionisation energy (IE1) of hydrogen has been calculated as 1313 kJ mol−1
