A hydrogen-like lithium ion, Li ( )

CHEMISTRY · Multi-part · AP · Chemistry · Atomic Structure and Properties · Atomic Structure and Properties

Problem

A hydrogen-like lithium ion, Li

^{2+}

(

Z=3

), undergoes an electronic transition from the state with principal quantum number

n=4

to a lower state with

n=2

. Assume the nucleus is infinitely massive and the motion is non-relativistic. Useful data: • Rydberg constant for hydrogen

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

• Planck’s constant

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

• Speed of light

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

•

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

(a) Determine the energies of the

n=4

and

n=2

levels of Li

^{2+}

in electron-volts. Show all work. (b) Calculate the energy difference

\Delta E

between these levels and determine the wavelength

\lambda

of the photon emitted during the transition. (c) Indicate the region of the electromagnetic spectrum (e.g. infrared, visible, ultraviolet, x-ray) in which this photon lies and briefly justify your choice based on its wavelength.

Related theory

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