Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsAtoms3 Marks
Question
What is Rydberg constant ? Write down its unit.
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Answer
Rydberg's constant: According to Bohr's model of hydrogen atom the energy of hydrogen like atoms in their nth energy level is expressed as follows: $E_{n}=-\left(\frac{me^{4}}{8{\in_{0}}^{2}h^{3}c}\right).Z^{2}.\left(\frac{hc}{n^{2}}\right)$ where $c=$ speed of light in vacuum. Since all the quantities involved in the term $\left(\frac{me^{4}}{8\in_{0}^{2}h^{3}c}\right)$ are universal constants, hence this term has a universal constant value. Therefore, this new constant term is known as Rydberg's constant and is denoted by R. Therefore, the above equation for $E_{n}$ can also be written as follows: $E_{n}=-\left(\frac{Rhc}{n^{2}}\right)Z^{2}$ Value of Rydberg's constant : $R=\frac{me^{2}}{8\in_{0}^{2}h^{3}c}$ $\Rightarrow R=\left[\frac{(9.1\times10^{-31})(1.6\times10^{-19})^{2}}{8(8.856\times10^{-12})^{2}(6.625\times10^{-34})(3\times10^{8})}\right]m^{-1}$ ⇒ $R=1.030\times10^{7}m^{-1}$ But this value of R is very close to the value of $R=1.097\times10^{7}m^{-1}$ calculated from impirical Balmer formula. This agreement provides a direct and striking confirmation of Bohr's Hydrogen model. Thus the standard value of R is taken as $R=1.097\times10^{7}m^{-1}.$ The S.I. unit of Rydberg's constant is metre$^{-1}$.
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