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
