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

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

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

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

Step-by-step explanation:

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

`E_n =( -13.6 * Z)/(n^2)`

where;

lithium Z = 3

therefore, the energy levels for Li²⁺ are

n=1 , n=2, n= 3

`E_1 =( -13.6 * 3)/(1^2)`

`E_1 = -13.6 * 3`

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

`E_2=( -13.6 * 3)/(2^2)`

`E_2=( -13.6 * 3)/(4)`

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

`E_3=( -13.6 * 3)/(3^2)`

`E_3=( -13.6 * 3)/(9)`

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