The Paschen series of hydrogen consists of all radiations produced when electrons…

CHEMISTRY · Subjective · CBSE · Chemistry · Structure of Atom · Structure of Atom

Problem

The Paschen series of hydrogen consists of all radiations produced when electrons fall to the stationary state having principal quantum number

n_f=3

. (a) Derive an expression for the wavelength

\lambda_n

of the line produced when an electron jumps from an initial level

n_i=n>3

to the level

n_f=3

. (b) Using your expression, obtain the shortest wavelength limit

(\lambda_{\text{min}})

of the Paschen series and calculate its numerical value. (c) Determine the wavelength of the first Paschen line

(n_i=4)

and hence compute the ratio

\dfrac{\lambda_{\text{first}}}{\lambda_{\text{min}}}

. Comment briefly on the significance of this ratio with respect to the spacing of lines in the series.