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The unit of Rydberg constant is ______.

Asked in GSEB Board March 2016 · Spectral series and wavelengths

(1) m
(2) Ryd
(3) m⁻¹
(4) eV

Answer: (3) m⁻¹

Step-by-step solution

Idea: the Rydberg constant appears in the wavelength formula 1/λ=R(1/(n₁²)-1/(n₂²)).

The bracket contains only quantum numbers, so it is a pure number.

Therefore R has the same unit as 1/λ.

Unit of R: m⁻¹ (its value is R=1.097×10⁷ m⁻¹).

Why the other options are wrong

(1) m is the unit of the wavelength itself; R multiplies a pure number to give 1/λ, so it carries the reciprocal unit.
(2) Ryd names the rydberg, an energy unit equal to Rhc≈13.6 eV; it is not the unit of the constant R, which is a wave number.
(4) eV is the unit of the energy Rhc=13.6 eV; the constant R on its own carries no hc.

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