A) \[{{E}_{3}}=\frac{16E}{3}\]
B) \[{{E}_{3}}=\frac{16E}{9}\]
C) \[{{E}_{3}}=\frac{4E}{9}\]
D) \[{{E}_{3}}=\frac{4E}{3}\]
Correct Answer: B
Solution :
The energy for nth orbit in the atom of atomic number (Z) is given by \[{{E}_{n}}=\frac{{{Z}^{2}}}{{{n}^{2}}}{{E}_{0}}\] So, for helium (Z = 2) and n = 3 \[\therefore \] for third orbit \[{{E}_{3}}=\frac{4}{9}{{E}_{0}}\] ?(1) Now for H atom (Z = 1) and n = 2 \[\therefore \] for second orbit \[{{E}_{2}}=\frac{1}{4}{{E}_{0}}\] ?(2) Now from Eqs. (1) and (2), we obtain \[\frac{{{E}_{3}}}{{{E}_{2}}}=\frac{\frac{4}{9}{{\varepsilon }_{0}}}{\frac{1}{4}{{E}_{0}}}=\frac{16}{9}\]or \[{{E}_{3}}=\frac{16}{9}{{E}_{2}}=\frac{16}{9}E\]
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