Question

The Bohr theory can be extended to non-hydrogen one electron ions such as He+ and Li2+, in which case the energy depends on the different atomic numbers Z for the respective atom. How much energy in Joules is required to excite the electron in Li2+ from n = 1 to n = 2?

Answer 1

Answer:

E =  1.5 x 10⁻¹⁷ J

Explanation:

The Rydberg equation for electronic transitions in the hydrogen atom  is

1//λ = Rh x ( 1/n₁² - 1/n₂²)

where            

           Rh : Rydberg´s constant 1.09737 x 10 ⁷ m⁻¹

           n₁ : Intial energy Level

           n₂ : Final energy Level

But for non-hydrogen one electron ions  such as He+ and Li2+ ²⁺ , the equation is similar but multiplied by Z²:

     1/ λ = Rh Z² x ( 1/n₁² - 1/n₂²)

I will work this problem by fist calculating 1/λ  and then use the equation E= hc/λ  where

h : Planck´s constant  6.626 x 10 ⁻³⁴ J s

c : Speed of light 3 x 10 ⁸

1/ λ =   1.09737 x 10 ⁷ m⁻¹ ( 3² ) x ( 1/1² - 1/2² )

1/ λ =   7.4 x 10⁷ m⁻¹

E = 6.626 x 10 ⁻³⁴ J s  x  3 x 10^8  m/s x   7.4 x 10⁷ m⁻¹

E =  1.5 x 10⁻¹⁷ J