IGNOU CHE 1 2018 - Calculate the ionization energy of hydrogen atom using Bohr’s th

Question

Calculate the ionization energy of hydrogen atom using Bohr’s theory.

24 Jan 2018

Answer :

Word Count : 1167

Rydberg equation for the hydrogen atom, which looks like this

Image ignouacademy-com--p-ionization-55686

Here

λe is the wavelength of the emitted photon (in a vacuum)
R is the Rydberg constant, equal to 1.097⋅107 m−1
n1 represents the principal quantum number of the orbital that is lower in energy
n2 represents the principal quantum number of the orbital that is higher in energy

In your case, you have

Image ignouacademy-com--p-calculate-24049

Image ignouacademy-com--p-energy-25345

This implies that the Rydberg equation will take the form

Image ignouacademy-com--p-using-64734

which, in your case, will get you

Image ignouacademy-com--p-ignou-34683

Rearrange to solve for the wavelength

Plug in the value you have for R to get

Image ignouacademy-com--p-atom-53350

Now, in order to find the energy that corresponds to this transition, calculate the frequency, ν, of a photon that is emitted when this transition takes place by using the fact that wavelength and frequency have an inverse relationship described by this equation

Here

ν is the frequency of the photon
c is the speed of light in a vacuum, usually given as 3⋅108 m s−1

Rearrange to solve for the frequency and plug in your value to find

Image ignouacademy-com--p-atom-44681

Finally, the energy of this photon is directly proportional to its frequency as described by the Planck - Einstein relation

Here

E is the energy of the photon
h is Planck's constant, equal to 6.626⋅10−34J s

Plug in your value to find

Image ignouacademy-com--p-atom-41369

This means that in order to remove the electron from the ground state of a hydrogen atom in the gaseous state and create a hydrogen ion, you need to supply 2.181⋅10−18 J of energy.

This means that for 1 atom of hydrogen in the gaseous state, you have

Now, the ionization energy of hydrogen represents the energy required to remove 1 mole of electrons from 1 mole of hydrogen atoms in the gaseous state.

To convert the energy to kilojoules per mole, use the fact that 1 mole of photons contains 6.022⋅1023 photons as given by Avogadro's constant.

You will end up with

Image ignouacademy-com--p-hydrogen-10894

You can thus

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