Question

What is the wavelength of the line corresponding to n=4 in the balmer series? express your answer in nanometers to three significant figures?

Answer 1

Expression for the Balmer series to find the wavelength of the spectral line is as follows:
1 / λ = R
`((1)/(2^(2) ) - (1)/( n^(2)) )`
Where, λ is wavelength, R is Rydberg constant, and n is integral value (4 here → Fourth level)
Substitute 1.097 x 10⁷ m⁻¹ for R and 4 for n in the above equation
1 / λ = (1.097 x 10⁷ m⁻¹)
`((1)/(2^(2) ) - (1)/(4^(2) ) )`
= 0.20568 x 10⁷ m⁻¹
λ = 4.86 x 10⁻⁷ m
since 1 m = 10⁹ nm
λ = 486 nm