(a) Starting from the expression for the energy of the th stationary orbit of a…

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

Problem

(a) Starting from the expression

E_n=-\dfrac{13.6\,Z^{2}}{n^{2}}\,\text{eV}

for the energy of the

n

th stationary orbit of a hydrogen-like ion, derive an expression for the wavelength

\lambda

of the photon emitted when the electron jumps from an initial orbit

n_i

to a lower orbit

n_f

(n_i>n_f)

. (b) Using the expression obtained in part (a), calculate the wavelength (in nm) of the photon emitted when an electron in a

\mathrm{Li^{2+}}

ion

(Z=3)

makes a transition from

n_i=4

n_f=2

. Take

R_H=1.097\times10^{7}\,\text{m}^{-1}

. (c) State to which region of the electromagnetic spectrum this radiation belongs.