Answer :
Answer:
[tex]\mathbf{\lambda = 1.01 \times 10^{3} \ nm}[/tex]
Explanation:
To determine the wavelength; let's first calculate the energy (E) change of the transition by using the Rydberg constant [tex](R_H)[/tex]
[tex]\Delta E = R_H ( \dfrac{1}{n_i^2}- \dfrac{1}{n_f^2})[/tex]
[tex]\Delta E = 2. 18 \times 10^{-18} \ J ( \dfrac{1}{7^2}- \dfrac{1}{3^2})[/tex]
[tex]\Delta E = 1.977 \times 10^{-19 } \ J[/tex]
Now; to calculate the wavelength by using the formula:
[tex]\lambda = \dfrac{c*h}{\Delta E}[/tex]
[tex]\lambda = \dfrac{(3.00 \times 10^8 \ m/s) *(6.63 \times 10^{-34} \ J.s)}{1.977 \times 10^{-19 } \ J}[/tex]
[tex]\lambda = 1.01 \times 10^{-6} \ m[/tex]
To nanometers; we have:
[tex]\lambda = 1.01 \times 10^{-6} \ m \times \dfrac{1 \ nm}{ 1 \times 10^{-9} \ m}[/tex]
[tex]\mathbf{\lambda = 1.01 \times 10^{3} \ nm}[/tex]