use the Rydberg equation to calculate the wavelength (in A) of the photon absorbed when a hydrogen atom undergoes a transition from n=1 to n=3.
and your question is....
The use of the equation is rather straighforward.
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To calculate the wavelength of the photon absorbed during a transition from n=1 to n=3 in a hydrogen atom, we can use the Rydberg equation. The Rydberg equation is:
1/λ = R * (1/n₁² - 1/n₂²)
Where:
- λ is the wavelength of the absorbed/emitted photon.
- R is the Rydberg constant (approximately 1.097 × 10^7 m⁻¹).
- n₁ is the initial energy level (n=1 in this case).
- n₂ is the final energy level (n=3 in this case).
To convert the wavelength from meters to Angstroms, we'll need to multiply the final result by 10^10 since there are 10^10 Angstroms in a meter.
Now, let's substitute the values into the equation and solve it:
1/λ = (1.097 × 10^7 m⁻¹) * (1/1² - 1/3²)
1/λ = (1.097 × 10^7 m⁻¹) * (1/1 - 1/9)
1/λ = (1.097 × 10^7 m⁻¹) * (8/9)
1/λ = 8.663 × 10^6 m⁻¹
Now, to convert this to Angstroms:
1/λ = 8.663 × 10^6 m⁻¹ * (10^10 Å/1 m)
Simplifying this expression gives us:
1/λ = 8.663 × 10^16 Å⁻¹
Finally, taking the reciprocal of both sides gives us:
λ = 1/(8.663 × 10^16 Å⁻¹)
Which is approximately:
λ = 1.155 × 10^-17 Å
So, the wavelength (λ) of the photon absorbed during this transition is approximately 1.155 × 10^-17 Angstroms.