According to the Bohr theory,the allowed energy states for the hydrogen atom are given by the relation This formula can be readily extended to other hydrogenic (one-electron)systems.The energy of the second level (n = 2)for the doubly ionized lithium atom is
A)-54.4 eV
B)13.6 eV
C)-30.6 eV
D)-3.4 eV
E)-1.5 eV

Question

According to the Bohr theory,the allowed energy states for the hydrogen atom are given by the relation  This formula can be readily extended to other hydrogenic (one-electron)systems.The energy of the second level (n = 2)for the doubly ionized lithium atom is
A)-54.4 eV 
B)13.6 eV 
C)-30.6 eV 
D)-3.4 eV 
E)-1.5 eV

Quizplus · Accepted Answer

The energy of a hydrogen atom in the n-th level is given by E_n = -13.6/n^2 eV. However, for a hydrogenic system with Z protons in the nucleus, the energy becomes E_n = -13.6 Z^2/n^2 eV.

For the doubly ionized lithium atom (Li2+), Z = 3. Thus, the energy of the n=2 level is E_2 = -13.6(3^2)/2^2 = -30.6 eV. Therefore, the correct choice is (C).

According to the Bohr Theory,the Allowed Energy States for the Hydrogen