question_answer 12)

Calculate the energy associated with the first orbit of\[H{{e}^{+}}\]. What is the radius of the orbit?

Answer:

Information shadow: n = 1, first orbit Z = 2, for \[H{{e}^{+}}\] Problem solving strategy: \[E=-\frac{{{Z}^{2}}}{{{n}^{2}}}\times 2.18\times {{10}^{-18}}\text{J}\] (Energy of hydrogen-like species) \[r=\frac{{{n}^{2}}}{Z}\times 0.529\overset{{}^\circ }{\mathop{\text{A}}}\,\] (Radius of nth orbit of hydrogen-like species) Working it out: \[E=-\frac{{{2}^{2}}}{{{1}^{2}}}\times 2.18\times {{10}^{-18}}=-8.72\times {{10}^{-18}}J\] \[r=\frac{{{1}^{2}}}{2}\times 0.529\overset{{}^\circ }{\mathop{\text{A}}}\,=0.2645\overset{{}^\circ }{\mathop{\text{A}}}\,\]