By using the Rydberg equation, the wavelength (in nm) of the photon emitted is 434 nanometer when it undergoes transition from n=5 to n=2.
The Rydberg equation is:
1/λ = RZ²(1/n₁² - 1/n₂²)
where,
λ is the wavelength of the photon (wavenumber = 1/wavelength)
R = Rydberg's constant = [tex]1.090[/tex]×[tex]10[/tex]⁷ [tex]m[/tex]⁻¹
Z = atomic number of the atom
n₁ and n₂ are integers where n₂> n₁.
putting the values in the formula we get,
1/λ =1.097×10⁷ m⁻¹ ×( 1 /2² - 1/5² )
1/λ = 1.097 × 10⁷ m⁻¹ × (1/4 -1/25)
1/λ = 1.097 × 10⁷ × (0.25 - 0.04)
1/λ = 1.097 × 10⁷ × 0.21
1/λ = 2289000
λ = 1/ 2289000
λ = 4.37×10⁻⁷ m
After that, we can now convert this wavelength to nm.
λ = 4.37×10⁻⁷/10⁻⁹
λ = 434 nm
Wavelength = 434nm
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