Respuesta :
Answer:
1024Å
Explanation:
The Rydberg equation is an empirical relationship equation expressed by Balmer and Rydberg which is given as:
1/λ = [tex]R_{H} (\frac{1}{n_{f} ^{2} }-\frac{1}{n_{i} ^{2} } )[/tex].............................(1)
where [tex]R_{H}[/tex] is the Rydberg constant given as [tex]1.09 x 10^{7}m^{-1}[/tex], n is the transition level and the subscript f and i show the final and initial level numbers respectively. λ is the wavelength.
[tex]n_{f}[/tex]= 1
[tex]n_{i} = 3[/tex]
Using equation (1), we have
1/λ [tex]= 1.097 x 10^{7}(\frac{1}{3^{2} }- \frac{1}{1^{2} })[/tex]
= [tex]1.097 x 10^{7} (\frac{1}{9} -\frac{1}{1} )[/tex]
= [tex]1.097 x 10^{7}(0.11-1)[/tex]
= [tex]1.097 x 10^{7} (-0.89)[/tex]
= - 9763300
λ = [tex]-\frac{1}{9763300}[/tex]
= [tex]-1.024x 10^{-7}m[/tex]
We should note that the negative sign we have is as a result of photon absorption whereby the hydrogen atom gains energy to undergo a transition from the lower energy level to a higher one. Wavelength does not have a negative value.
To convert to Å, we have
λ = [tex]\frac{1.024 x 10^{-7} }{10^{-10} }[/tex] = 1024Å
Therefore the wavelength of the photon in Å is 1024Å
The wavelength (in Å) of the photon absorbed when a hydrogen atom undergoes a transition from n = 1 to n = 3.λ is; 10.25 × 10⁹ Å
How to use Rydeberg equation?
The energy levels are given as be n = 1 and n = 3. Rydberg's equation will allow us calculate the wavelength of the photon absorbed by the electron during this transition. The formula is;
1/λ = R(1/n₂² - 1/n₁²)
where;
λ is wavelength
n₂ is final energy level
n₁ is initial energy level
R is rydberg's constant = 1.0974 * 10⁷ m⁻¹
Thus;
1/λ = (1.0974 * 10⁷)(1/1² - 1/3²)
1/λ = 1.0974 * 10⁷ * (8/9)
1/λ = 0.975 * 10⁷
λ = 1.025 × 10⁻⁷ m = 10.25 × 10⁹ Å
Use more about Rydeberg Equation at; https://brainly.com/question/17867710
