Question

The energy in joules of an atom is given by $E_n=-(2.18\times {10}^{-18})\frac{Z^2}{n^2}$, where $Z$ is the atomic number of the atom and $n$ is the orbit number.Which of the following equations gives the atomic number of an atom given the energy of its nth orbit (assuming there is a single electron in that orbit)?

• A. $Z={10}^9\sqrt{-\frac{n^2{E}_n}{2.18}}$
• B. $Z=\frac{1}{{10}^9}\sqrt{-\frac{n^2{E}_n}{2.18}}$
• C. $Z={10}^9\sqrt{-\frac{2.18E_n}{n^2}}$
• D. $Z=\frac{1}{{10}^9}\sqrt{-\frac{2.18E_n}{n^2}}$

Answer 1

Answer: (A)

$Z={10}^9\sqrt{-\frac{n^2{E}_n}{2.18}}$

Given, $E_n=-(-2.18\times {10}^{-18})\frac{z^2}{n^2}$
Isolate $z^2$ from the above equation, we get
$Z^2=\sqrt{-\frac{n^2{E}_n}{2.18\times {10}^{-9}\times {10}^{-9}}}$
So, $Z^2={10}^9\sqrt{-\frac{n^2{E}_n}{2.18}}$