question_answer 35)

(i) The energy associated with the first orbit of hydrogen atom is \[-2.18\times {{10}^{-18}}J\]. What is the energy associated with the fifth orbit? (ii) Calculate the radius of Bohr's fifth orbit of hydrogen atom.

Answer:

(i) \[{{E}_{n}}=\frac{-{{E}_{1}}}{{{n}^{2}}}\] \[=\frac{-2.18\times {{10}^{-18}}}{25}\] \[=-8.72\times {{10}^{-20}}J\] (ii) \[r=\frac{{{n}^{2}}}{Z}\times 0.529\overset{{}^\circ }{\mathop{\text{A}}}\,\] \[=\frac{25}{1}\times 0.529\overset{{}^\circ }{\mathop{\text{A}}}\,\] \[=13.225\,\overset{\text{o}}{\mathop{\text{A}}}\,\] or 1.3225 nm