2 April, 12:30

# 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?

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1. 2 April, 12:59
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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