Introduction:
The Rydberg constant is a physical constant that appears in the formula for the wavelengths of light emitted by hydrogen atoms. It is named after the Swedish physicist Johannes Rydberg, who first derived the formula in 1888.

Two values of Rydberg constant:
There are two values of the Rydberg constant that are commonly used: 109,677 cm^-1 and 2.18×10^-18 J. Both values are accurate, but they are used in different contexts.

Using 109,677 cm^-1:
The value of 109,677 cm^-1 is commonly used in spectroscopy, where the wavelengths of light are measured in units of cm^-1. This value is derived from the original formula for the Rydberg constant, which was based on the Balmer series of hydrogen spectral lines.

Using 2.18×10^-18 J:
The value of 2.18×10^-18 J is commonly used in chemistry problems, where the energies of photons and electrons are measured in units of joules. This value is derived from the original formula for the Rydberg constant, which relates the energies of the electron in the hydrogen atom to the wavelengths of the light it emits.

Conclusion:
In conclusion, both values of the Rydberg constant are accurate, but they are used in different contexts. When working with spectroscopy, it is appropriate to use 109,677 cm^-1, while in chemistry problems, it is appropriate to use 2.18×10^-18 J. It is important to use the correct value in order to get accurate results.

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