How much energy would it take to remove the electron from unexcited hydrogen completely so that it is no longer bound to its proton?

Modern Physics
3rd Edition
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Chapter4: The Particle Nature Of Matter
Section: Chapter Questions
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The light observed that is emitted by a hydrogen atom is explained by a simple model of its structure with one proton in its nucleus and an electron bound to it, but only with internal energies of the atom  satisfying

EH=−RH/n2EH=−RH/n2

where RHRH is the Rydberg constant and nn is an integer such as 1, 2, 3 ... and so on.  When a hydrogen atom in an excited state emits light, the photon carries away energy and the atom goes into a lower energy state. 

Be careful about units.  The Rydberg constant in eV is 

13.605693009 eV  

That would be multiplied by the charge on the electron 1.602× 10-19 C to give 

2.18× 10-18  J

A photon with this energy would have a frequency f such that E=hf.  Its wavelength would be λ = c/f = hc/E.  Sometimes it is handy to measure the Rydberg constant in units of 1/length for this reason.  You may see it given as 109737 cm-1 if you search the web, so be aware that's not joules.

The following questions are intended to help you understand the connection between the structure of atoms such as hydrogen and the spectrum of light that they emit.  

 

Answer these and explain your reasoning.

1. How much energy would it take to remove the electron from unexcited hydrogen completely so that it is no longer bound to its proton?  

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