question_answer

Based on equation \[E=-2.178\times {{10}^{-18}}J\left( \frac{{{Z}^{2}}}{{{n}^{2}}} \right)\]certain con-elusions are written. Which of them is not correct?                                                                                            [NEET 2013]

A)  The negative sign in equation simply means that the energy of electron bound to the nucleus is lower than it would be if the electrons were at the infinite distance from the nucleus

B)  Larger the value of n, the larger is the orbit radius

C)  Equation can be used to calculate the change in energy when the electron changes orbit

D)  For \[n=1\] the electron has a more negative energy than it does for \[n=6\] which means that the electron is more

Correct Answer: D Solution : loosely bound in the smallest allowed orbit

If          \[n=1,\]

\[{{E}_{1}}=-2.178\times {{10}^{-18}}{{Z}^{2}}J\]

In         \[n=6\]

\[{{E}_{6}}=\frac{-2.178\times {{10}^{-18}}{{Z}^{2}}}{36}\]

\[=6.05\times {{10}^{-20}}{{Z}^{2}}J\]

From the above calculation, it is obvious that electron has a more negative energy than it does for \[n=6\]. It means that electron is more strongly bound in the smallest allowed orbit.