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 levels of a one-electron atom are given by:

$E_n = -\frac{Z^2}{n^2}	imes13.6	ext{ eV}$

where $Z$ is the atomic number of the nucleus and $n$ is the principal quantum number (n=1,2,3,...).

For the doubly ionized lithium atom (Li$^{2+}$), $Z=3$, so the energy of the second level can be calculated as follows:

$E_2 = -\frac{(3)^2}{2^2}	imes13.6	ext{ eV} = -30.6	ext{ eV}$

Therefore, the best choice is C.

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