Respuesta :
The wavelength of the line in the hydrogen atom spectrum corresponding to the n₁ = 2 to n₂ = 6 transition is 4102 nm.
What is Rydberg Formula?
When an electron transitions from a higher to a lower energy level, it discharges a photon of the a specific wavelength. The Rydberg formula describes the connection between the shift in energy level and the wavelength:
[tex]\frac{1}{\lambda}=R\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)[/tex]
Where,
R = Rydberg constant ( = 1.097 × 10⁷ /m)
n₁ = lower energy level ( = 2)
n₂ = higher energy level ( = 6)
λ = wavelength of emitted photon
Now, according to the question;
Substitute the given values in the formula;
[tex]\begin{aligned}&\frac{1}{\lambda}=R\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right) \\&\frac{1}{\lambda}=1.097 \times 10^{7}\left(\frac{1}{2^{2}}-\frac{1}{6^{2}}\right)\end{aligned}[/tex]
[tex]\begin{aligned}&\frac{1}{\lambda}=2.437 \times 10^{6} \\&\lambda=4.102\times 10^{-6}\end{aligned}[/tex]
λ = 4102 nm.
Therefore, the wavelength of the line in the hydrogen atom spectrum corresponding to the n₁ = 2 to n₂ = 6 transition is 4102 nm.
To know more about Rydberg Formula, here
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