Hydrogen-like atoms of element Z have discrete energy levels

CHEMISTRY · Multi-part · CBSE · Chemistry · Structure of Atom · Structure of Atom

Problem

Hydrogen-like atoms of element Z have discrete energy levels. For a ground-state atom of element Z, the minimum photon energy required for ionization is experimentally found to be

13.6\,\text{eV}

. A second experiment shows that photons of wavelength

364\,\text{nm}

are just sufficient to ionize an atom that has first been excited to its first excited state. Constants:

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

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

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

. (a) Using the ground-state ionization value, compute the longest wavelength that can ionize a ground-state atom of element Z. Express your answer to three significant figures. (b) Determine the energy (in electron-volts) of a photon with wavelength

364\,\text{nm}

. (c) Using your answers from parts (a) and (b), calculate the energy difference between the ground state and the first excited state of element Z. (d) When an atom in the first excited state returns directly to the ground state, a photon is emitted. Determine the wavelength of this emitted photon and comment on whether it lies in the ultraviolet, visible, or infrared region of the electromagnetic spectrum.

Related theory

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