Answer:
[tex]4.86\times10^{-7}\ \text{m}[/tex]
Explanation:
R = Rydberg constant = [tex]1.09677583\times 10^7\ \text{m}^{-1}[/tex]
[tex]n_1[/tex] = Principal quantum number of an energy level = 2
[tex]n_2[/tex] = Principal quantum number of an energy level for the atomic electron transition = 4
Wavelength is given by the Rydberg formula
[tex]\lambda^{-1}=R\left(\dfrac{1}{n_1^2}-\dfrac{1}{n_2^2}\right)\\\Rightarrow \lambda^{-1}=1.09677583\times 10^7\left(\dfrac{1}{2^2}-\dfrac{1}{4^2}\right)\\\Rightarrow \lambda=\left(1.09677583\times 10^7\left(\dfrac{1}{2^2}-\dfrac{1}{4^2}\right)\right)^{-1}\\\Rightarrow \lambda=4.86\times10^{-7}\ \text{m}[/tex]
The wavelength of the light emitted is [tex]4.86\times10^{-7}\ \text{m}[/tex].
