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

E = 1.5 x 10⁻¹⁷ J

Step-by-step 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