Respuesta :
Answer:
The answer is 434nm
Explanation:
The Rydberg equation is an empirical relationship expressed by Balmer and Rydberg which is stated as:
1/λ = [tex]R_{H} (\frac{1}{n_{f} ^{2} }-\frac{1}{n_{i} ^{2} } )[/tex].............................. (1)
where λ is the wavelength, [tex]R_{H}[/tex] is the Rydberg constant equal to [tex]1.097 x 10^{7}m^{-1}[/tex], n is the transition level number, the subscript f and i are the final and initial levels respectively. Therefore for final transition n = 2 and for initial transition n = 5.
Making substitutions into equation (1), gives
1/λ = [tex]1.097 x 10^{7} (\frac{1}{2^{2} }-\frac{1}{5^{2} })[/tex]
= [tex]1.097 x 10^{7} (\frac{1}{4} - \frac{1}{25} )[/tex]
= [tex]1.097 x 10^{7} (0.25 - 0.04)[/tex]
= [tex]1.097 x 10^{7} x 0.21[/tex]
= 2303700
∴ λ = [tex]\frac{1}{2303700}[/tex] [tex]= 4.34 x 10^{-7}m[/tex]
Converting to nm, we have
λ = [tex]\frac{4.34 x 10^{-7} }{10^{-9} } = 434nm[/tex]
Therefore, the wavelength of the emitted photon is 434nm
By using the Rydberg equation, the wavelength (in nm) of the photon emitted is 434 nanometer.
Given the following data:
Initial transition = 5
Final transition = 2
Rydberg constant = [tex]1.090 \times 10^7 \;m^{-1}[/tex]
To calculate the wavelength (in nm) of the photon emitted by using the Rydberg equation:
Mathematically, the Rydberg equation is given by the formula:
[tex]1/\lambda = R(\frac{1}{n_f^2} - \frac{1}{n_f^2} )[/tex]
Where:
- [tex]\lambda[/tex] is the wavelength.
- R is the Rydberg constant.
- [tex]n_f[/tex] is the final transition.
- [tex]n_i[/tex] is the initial transition.
Substituting the given parameters into the formula, we have;
[tex]1/\lambda = 1.090 \times 10^7 (\frac{1}{2^2} - \frac{1}{5^2} )\\\\1/\lambda = 1.090 \times 10^7 (\frac{1}{4} - \frac{1}{25} )\\\\1/\lambda = 1.090 \times 10^7 (0.25 - 0.04)\\\\1/\lambda = 1.090 \times 10^7 \times 0.21\\\\1/\lambda = 2,289,000\\\\\lambda = \frac{1}{2,289,000} \\\\\lambda = 4.37 \times 10^{-7} \; meters[/tex]
To nanometer:
[tex]\lambda = \frac{4.37 \times 10^{-7}}{10^{-9}}\\\\\lambda = 434 \;nanometer[/tex]
Wavelength = 434 nanometer.
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