Wavelength of photon emitted due to transition in H-atom \\\\(\\dfrac{1}{\\lambda} = R \\bigg( \\dfrac{1}{n_1^2} - \\dfrac{1}{n_2^2} \\bigg)\\\\)Shortest wavelength is emitted in Balmer series if the transition of electron takes place from \\\\(n_2 = \\infty\\\\) to \\\\(n_1 = 2\\\\).\\\\(\ herefore\\\\) Shortest wavelength in Balmer series \\\\(\\dfrac{1}{\\lambda_s} = R \\bigg( \\dfrac{1}{2^2} - \\dfrac{1}{\\infty} \\bigg)\\\\)Or \\\\(\\lambda_s = \\dfrac{4}{R}\\\\)\\\\(\\implies\\\\) \\\\(\\lambda_s = \\dfrac{4}{1.097 \ imes 10^{7}} = 364.6 nm\\\\)Longest wavelength is emitted in Balmer series if the transition of electron takes place from \\\\(n_2 = 3\\\\) to \\\\(n_1 = 2\\\\).\\\\(\ herefore\\\\) Longest wavelength in Balmer series \\\\(\\dfrac{1}{\\lambda_L} = R \\bigg( \\dfrac{1}{2^2} - \\dfrac{1}{3^2} \\bigg)\\\\)Or \\\\(\\lambda_s = \\dfrac{36}{5R}\\\\)\\\\(\\implies\\\\) \\\\(\\lambda_s = \\dfrac{36}{5\ imes 1.097 \ imes 10^{7}} = 656.3 nm\\\\)