Why will the energy be minimum when the wavelength will be maximum and vice versa? Logic of relation of longest and shortest wavelengths with energy of the emitted photons in Paschen series.  

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You are describing the normal pattern of occurrence with waves on the electromagnetic spectrum.  If you start at the lower left end of the spectrum, you have the waves that are lowest in energy, called radio waves.  The wavelengths of these waves are very long.  Wavelength is the number of waves passing per second.  So lets think about this:  a low number on wavelength would mean fewer waves are passing per second, which means these waves possess lower energy.  As you progressively move up the electromagnetic spectrum, each passing wavelength becomes shorter, meaning the waves have more energy, so there are more of them passing per second.  Visible light is right in the middle of the EM spectrum, so the wavelengths of visible light are higher in energy than those of radio waves.  The gamma rays all the way at the right end of the EM spectrum are the highest energy waves.  They have the shortest wavelengths, which means there are more of them passing per second than all the other waves.

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