Answer: [tex]2.16\times 10^{-6}m[/tex]
Explanation:
Using Rydberg's Equation:
[tex]\frac{1}{\lambda}=R_H\left(\frac{1}{n_i^2}-\frac{1}{n_f^2} \right )\times Z^2[/tex]
Where,
= Wavelength of radiation
[tex]R_H[/tex] = Rydberg's Constant = [tex]10973731.6m^{-1}[/tex]
[tex]n_f[/tex] = Higher energy level = 7
= Lower energy level = 4
Z= atomic number = 1 (for hydrogen)
[tex]\frac{1}{\lambda}=10973731.6m^{-1}\left(\frac{1}{4^2}-\frac{1}{7^2} \right )\times 1^2[/tex]
[tex]\frac{1}{\lambda}=461904.5[/tex]
[tex]\frac{1}{\lambda}=461904.5[/tex]
[tex]\lambda=2.16\times 10^{-6}m[/tex]
Thus wavelength is [tex]2.16\times 10^{-6}m[/tex]
The wavelength of the transition from n = 7 to n=4 is 2166nm.
Using the Rydberg formula, we have;
1/λ = R(1/n^2f - 1/n^2i)
λ = wavelength
R = Rydberg constant = 1.097 × 10^7 m-1
nf = 4
ni = 7
Substituting values;
1/λ = 1.097 × 10^7 m-1(1/4^2 - 1/7^2)
1/λ = 2.166 × 10^7 m or 2166nm
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