The bohr theory of the hydrogen atom predicts the energy difference (in j) between the n= 3 and the n = 5 state to be

The Bohr model for the Hydrogen atom allows to calculate the result for the transition between the two levels is:

     ΔE = 0.9767 eV = 1.548 10⁻¹⁹ J

The Bohr atomic model for the hydrogen atom establishes that electrons rotate in circular stable orbits without emitting energy and uses Rutherford's model where all the mass of the atom is concentrated in a very small volume called nucleus, The energy of each electronic state is

            n= 1, 2, 3, ...

Where k is the Coulomb constant, e the electron charge, a₀ the Bohr radius and n an integer.

A transition occurs between two states with different atomic numbers.

   ΔE = - 13.606 (  )    [eV]

where the energy is expressed in electron-volts.

Let's look for the energy of the transition.

   ΔE = -13,606 (   )

   ΔE = 0.9767 eV

You can also reduce the result to Julio units even when it is not common.

   ΔE = 0.9757 eV (   ) = 1.548 10⁻¹⁹ J

This is an energy in the infrared range, in the attachment we can see a diagram of the hydrogen transition.

In conclusion, using the Bohr model for the Hydrogen atom we can calculate the result for the transition between the two levels is:

     ΔE = 0.9767 eV = 1.548 10⁻¹⁹ J

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Solution:

a theory of atomic structure in which the hydrogen atom is assumed to consist of a proton as nucleus, with a single electron moving in distinct circular orbits around it, each orbit corresponding to a specific quantized energy state.

the electron energy level of the hydrogen atom can be written as:  

En = -2.179×10^-18 J/ n^2  

Thus for n = 3: E3 = -2.421x10^-19 J  

For n = 5: E5 = -8.72x10^-20 J  

Hence the energy difference between the n=3 state & n=5 state is:  

2.421x10^-19J - 8.72x10^-20J  

     = 1.549x10^-19 J