Photons from two different transitions in the Lyman series of hydrogen are incident sequentially on the same metal surface. The first member of the Lyman series has wavelength and produces a stopping potential V₀ . The second member of the Lyman series produces a stopping potential V₁ . The difference in stopping potentials (V₁ - V₀) is

Step-by-step solution

For the Lyman series, the transitions terminate at n₁ = 1 . For the first member ( n=2 n=1 ): 1 = R ( 1 1^2 - 1 2^2 ) = 3R 4 R = 4 3 For the second member ( n=3 n=1 ), let the wavelength be ₂ : 1 ₂ = R ( 1 1^2 - 1 3^2 ) = 8R 9 Substituting R = 4 3 into the above equation: 1 ₂ = 8 9 ( 4 3 ) = 32 27 According to Einstein's photoelectric equation, the stopping potential V is given by eV = hc - W , where W is the work function. For the first member: eV₀ = hc - W For the second member: eV₁ = hc ₂ - W Subtracting the fir