Question

If our eyes could see a slightly wider region of the electromagnetic spectrum, we would see a fifth line in the Balmer series emission spectrum. Calculate the wavelength λλlambda associated with the fifth line.

Answer 1

Answer:

λ = 397 nm

Explanation:

given,

Rydberg wavelength equation for Balmer series

$\dfrac{1}{\lambda}=R(\dfrac{1}{n_f^2}-\dfrac{1}{n_i^2})$

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

$\dfrac{1}{\lambda}=(1.097\times 10^7)(\dfrac{1}{2^2}-\dfrac{1}{7^2})$

$\dfrac{1}{\lambda}=(1.097\times 10^7)(\dfrac{1}{2^2}-\dfrac{1}{7^2})$

$\dfrac{1}{\lambda}=2.5186\times 10^6$

$\lambda = 3.97\times 10^{-7}$

Hence, the wavelength is equal to  λ = 397 nm