The energy change associated with the transition from n = 2 to n = 5 in the hydrogen atom is 2.856 eV.
Planck's equation, E = h, relates the energy change connected to a transition to the frequency of the electromagnetic wave. The equation c = then links the wave's frequency to both its wavelength and the speed of light.
The expression for the change in energy for a transition from a state to a state in a hydrogen atom is
E = -13.6Z² (1/Nf² - 1/Ni²)
where Z is the atomic number, which is 1 for hydrogen. Substituting
Nf= 5 and Ni= 2
E = -13.6 × (1/ (5)²- 1/ (2)²)
E = -13.6 × - 0.21
E = 2.856 eV
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