Given below are two statements: Statement I: The wavenumber of the longest wavelength line in the Lyman series of He ^+ ion is equal to 3R_H . (where R_H is the Rydberg constant) Statement II: In the photoelectric effect, the maximum kinetic energy of the ejected photoelectrons depends on the intensity of the incident light. In the light of the above statements, choose the correct answer from the options given below:

Step-by-step solution

For the longest wavelength line in the Lyman series, the transition is from n₂ = 2 to n₁ = 1 . The wavenumber is given by Rydberg's formula: = R_H Z^2 ( 1 n₁^2 - 1 n₂^2 ) For He ^+ ion, Z = 2 . = R_H (2)^2 ( 1 1^2 - 1 2^2 ) = 4 R_H ( 1 - 1 4 ) = 4 R_H ( 3 4 ) = 3 R_H Thus, Statement I is true. In the photoelectric effect, the maximum kinetic energy of ejected photoelectrons is given by Einstein's photoelectric equation: K_ = h - K_ depends on the frequency of the incident light and the work function of the metal, b