Which of the following statement(s) is (are) correct about the...

For Balmer Series:

Shortest wavelength, $\dfrac{{E}_{o}}{4} = \dfrac{hc}{{\lambda}_{s}}$

Longest wavelength, \left(\dfrac{{E}_{o}}{4} - \dfrac{{E}_{0}}{9}\right) = \dfrac{hc}{{\lambda}_{l}} = \dfrac{5{E}_{o}}{36}$</p><p>$∴ \dfrac{{\lambda}_{l}}{{\lambda}_{s}} = \dfrac{9}{5}$</p><p>Range of energy level in Balmer series,</p><p>\left(\dfrac{5{E}_{0}}{36}, \dfrac{{E}_{0}}{4}\right)$

Range of energy level in Paschen series,

\left(\dfrac{7{E}_{0}}{144}, \dfrac{{E}_{0}}{9}\right)$</p><p>Hence, no overlap.</p><p>For Lyman series:</p><p>For shortest wavelength,</p><p>${E}_{0} = \dfrac{hc}{{\lambda}_{0}}$</p><p>For general wavelength,</p><p>\left({E}_{0} - \dfrac{{E}_{0}}{{n}^{2}}\right) = \dfrac{hc}{\lambda}$

$⇒ \dfrac{1}{\left(1 - \dfrac{1}{{n}^{2}}\right)} = \dfrac{\lambda}{{\lambda}_{0}}$

$∴ \lambda = \left(\dfrac{{n}^{2}}{{n}^{2} - 1}\right){\lambda}_{0}$

or $\lambda = \left(1 + \dfrac{1}{{n}^{2} - 1}\right){\lambda}_{0}= \left(1 + \dfrac{1}{{m}^{2}}\right){\lambda}_{0}$

as $m$ should be an integer.

Range of energy level in Lyman series, \left(\dfrac{3{E}_{0}}{4}, {E}_{0}\right)$</p><p>$⇒ Lyman and Balmer series wavelengths do not overlap.