The energy of an electron in the first Bohr orbit of hydrogen atom is -2.18 10-18 J. Its energy in the third Bohr orbit…

🧠 The Energy Well Inversion In the Bohr model, energy is inversely proportional to the square of the shell number ($n^2$). As you move further from the nucleus, the binding energy drops sharply.

🗺️ The Rydberg Path

1. Proportionality: $E_n \propto 1/n^2$.
2. Case: Comparison of Ground state ($n=1$) and 3rd orbit ($n=3$).
3. Calculation: $E_3 = E_1 \times \frac{1}{3^2} = \frac{E_1}{9}$

⚡ The "Denominator Square" Shortcut If shell number is tripled ($1 \to 3$), the energy must drop to $1/9\text{th}$. Just look at the integer and square it!

⚠️ Common Traps Picking "one third" (1/3). Linear scaling applies to velocity ($v \propto 1/n$); energy is siempre based on the square.

$\boxed{\text{Answer: 1/9th of the value}}$