Answer:
λ = 397 nm
Explanation:
given,
Rydberg wavelength equation for Balmer series
[tex]\dfrac{1}{\lambda}=R(\dfrac{1}{n_f^2}-\dfrac{1}{n_i^2})[/tex]
R is the Rydberg constant, R = 1.097 x 10⁷ m⁻¹
n_i = initial energy level
n_f = final energy level
where as for Balmer series n_f = 2
n_i = 7
[tex]\dfrac{1}{\lambda}=(1.097\times 10^7)(\dfrac{1}{2^2}-\dfrac{1}{7^2})[/tex]
[tex]\dfrac{1}{\lambda}=(1.097\times 10^7)(\dfrac{1}{2^2}-\dfrac{1}{7^2})[/tex]
[tex]\dfrac{1}{\lambda}=2.5186\times 10^6[/tex]
[tex]\lambda = 3.97\times 10^{-7}[/tex]
Hence, the wavelength is equal to λ = 397 nm
