Consider a hydrogen-like lithium ion (Li ) whose nucleus has charge number .

CHEMISTRY · Multi-part · A Level · Chemistry · Atomic structure · Atomic structure

Problem

Consider a hydrogen-like lithium ion (Li

^{2+}

) whose nucleus has charge number

Z = 3

. (a) Derive an expression, in terms of

Z

and the initial principal quantum number

n

(where

n

is even), for the wavelength of the photon emitted when the electron jumps from the

n

th orbit to the

\dfrac{n}{2}

th orbit. (b) Using your result, calculate the wavelength of the photon emitted when the electron in Li

^{2+}

makes the transition

n = 4 \rightarrow n = 2

. (c) Determine the frequency and the linear momentum of this photon. Take

h = 6.63\times10^{-34}\,\text{J\,s}

c = 3.00\times10^{8}\,\text{m\,s}^{-1}

and

1\,\text{eV} = 1.60\times10^{-19}\,\text{J}