The threshold wavelength of a photosensitive material is equal to the frequency of H _ a line of hydrogen. If a photon whose frequency equal to the frequency of H _ b line of hydrogen is incident on this photosensitive material, the maximum kinetic energy of the emitted photoelectrons is (R-Rydberg's constant, h- Flanck's constant and c- speed of light in vacuum)

Step-by-step solution

H _ line of Balmer series aligned & n ₂=3 to n ₁=2 & 1 ₀ = R ( 1 2^2 - 1 3^2 )= R ( 1 4 - 1 9 )= R [ 9-4 36 ] aligned 1 ₀ = 5 R 36 Here ₀ is the threshold frequency. H _ line of Balmer series aligned & n ₂=4 to n ₁=2 & 1 = R ( 1 2^2 - 1 4^2 )= R ( 1 4 - 1 16 ) & = R ( 4-1 16 )= 3 R 16 aligned Maximum, kinetic energy, K.E = h c - h c ₀ = hc [ 3 R 16 - 5 R 36 ]= 7 Rhc 144