Energy required for the electron excitation in Li++ from the first to the third Bohr orbit is :
\({E_1} = - \frac{{13.6{{(3)}^2}}}{{{{(1)}^2}}}\)
\({E_3} = - \frac{{13.6{{(3)}^2}}}{{{{(3)}^2}}}\)
\ DE = E3 – E1
\( = 13.6{(3)^2}\left[ {1 - \frac{1}{9}} \right]\)
\( = \frac{{13.6 \times 9 \times 8}}{9}\)
DE = 108.8 eV
The energy required for electron excitation in a hydrogen-like atom is calculated using the Bohr model formula for energy levels. For Li++ (lithium ion with +2 charge, meaning it has only one electron, making it hydrogen-like), the atomic number Z = 3.
The energy of an electron in the nth orbit is given by:
Step 1: Calculate the energy in the first orbit (n=1):
Step 2: Calculate the energy in the third orbit (n=3):
Step 3: The energy required for excitation from n=1 to n=3 is the difference:
Final Answer: 108.8 eV
Bohr's Model for Hydrogen-like Atoms: This model applies to atoms or ions with a single electron. The energy levels depend on the principal quantum number n and the atomic number Z.
Key Formula: Energy of electron in nth orbit:
Excitation Energy: The energy required to move an electron from a lower energy level (ni) to a higher energy level (nf) is ΔE = Ef - Ei.