Hydrogen atom in ground state is excited by a monochromatic radiation of λ = 975   Å . Number of spectral lines in the resulting spectrum emitted will be:

Step-by-step solution

Given weavelength is λ = 975 Å By Rydberg's equation for hydrogen atom is 1 λ = R 1 n 1 2 - 1 n 2 2 1 975 = R 1 1 - 1 n 2 2 ∵ n 1 = 1 for ground state where R is the Rydberg constant = 1 . 09 × 10 7   m - 1 Solving above equation, we get rounded numerical value n 2 = 4 (highest principal quantum number) Total number of spectral lines is given in terms of highest principal quantum number as = n ( n - 1 ) 2 = 4 ( 4 - 1 ) 2 = 6