# Problem: What is the change in energy, ΔE, in kilojoules per mole of hydrogen atoms for an electron transition from n = 7 to n = 2?The Rydberg equation expresses the wavelength, λ, of emitted light based on the initial and final energy states (ni and nf) of an electron in a hydrogen atom:1λ= RH×(1nf2-1ni2)where RH = 1.097 × 107 m− 1 = 1.097 × 10−2 nm−1.You may also see this equation written as1λ= -RH×(1ni2-1nf2)Since(1nf2-1ni2)=-(1ni2-1nf2)the two formulas are equivalent and sometimes used interchangeably. It can help to remember that when light is emitted, E is negative. When light is absorbed, E is positive.

###### Problem Details

What is the change in energy, ΔE, in kilojoules per mole of hydrogen atoms for an electron transition from n = 7 to n = 2?

The Rydberg equation expresses the wavelength, λ, of emitted light based on the initial and final energy states (ni and nf) of an electron in a hydrogen atom:

where RH = 1.097 × 107 m− 1 = 1.097 × 10−2 nm−1.

You may also see this equation written as

Since

$\left(\frac{1}{{{n}_{f}}^{2}}-\frac{1}{{{n}_{i}}^{2}}\right)\mathbf{=}\mathbf{-}\left(\frac{1}{{{n}_{i}}^{2}}-\frac{1}{{{n}_{f}}^{2}}\right)$

the two formulas are equivalent and sometimes used interchangeably. It can help to remember that when light is emitted, E is negative. When light is absorbed, E is positive.