Question

Consider a lithium nucleus, of charge +3q. Calculate the first three electron energies for an electron in a Li++ ion, using the Bohr model.

Answer 1

Answer:

$\mathbf{E_1 = -40.8 \ eV}$

$\mathbf{E_2= -10.2 \ eV}$

$\mathbf{E_3=-4.533 \e V}$

Explanation:

In an  hydrogen like atoms, the formula related to the  energy of an  nth quantum number is:

$E_n =\dfrac{ -13.6 \times Z}{n^2}$

where;

lithium Z = 3

therefore,  the energy levels for Li²⁺ are

n=1 , n=2, n= 3

$E_1 =\dfrac{ -13.6 \times 3}{1^2}$

$E_1 = -13.6 \times 3$

$\mathbf{E_1 = -40.8 \ eV}$

$E_2=\dfrac{ -13.6 \times 3}{2^2}$

$E_2=\dfrac{ -13.6 \times 3}{4}$

$\mathbf{E_2= -10.2 \ eV}$

$E_3=\dfrac{ -13.6 \times 3}{3^2}$

$E_3=\dfrac{ -13.6 \times 3}{9}$

$\mathbf{E_3=-4.533 \e V}$