Example 6.4: Calculating the Energy of an Electron in a Bohr Orbit
Calculating the Energy of an Electron in a Bohr Orbit
Early researchers were very excited when they were able to predict the energy of an electron at a particular distance from the nucleus in a hydrogen atom. If a spark promotes the electron in a hydrogen atom into an orbit with
\(n = 3\), what is the calculated energy, in joules, of the electron?
Solution
\(n\) \(= 3\)
The energy of the electron is given by this equation:
\(E = \dfrac{- k \cdot {Z}^{2}}{{n}^{2}}\)
The atomic number, Z, of hydrogen is
1 and k is
\(2.179\times 10^{-18 }\)J.
\(Z\) \(= 1\)
\(k\) \(= 2.179\times 10^{-18}\ \mathrm{J}\)
\(E\) \(= \dfrac{-k \cdot {Z}^{2}}{{n}^{2}}\)
\(\ \ \ =\dfrac{-2.179\times 10^{-18}\ \mathrm{J} \cdot {1}^{2}}{{3}^{2}}\)
\(\ \ \ =\dfrac{-2.1790\times 10^{-18}\ \mathrm{J} \cdot 1}{9}\)
\(\ \ \ =\dfrac{-2.1790\times 10^{-18}\ \mathrm{J}}{9}\)
\(\ \ \ =-2.421\times 10^{-19}\ \mathrm{J}\)