Question

Figure 37.7 identified the wavelengths of four lines in the Balmer series of hydrogen.

a. Determine the Balmer formula n and m values for these wavelengths.

b. Predict the wavelength of the fifth line in the spectrum

Short answer

(a) The Balmer formula is $\lambda =\frac{91.18}{{\displaystyle \frac{1}{m^2}}-{\displaystyle \frac{1}{n^2}}}nm$

(b) Wavelength of the fifth line in the spectrum = 397.139 nm

Step-by-step solution

part(a) Step 1: Given information

we have given the emission spectrum of hydrogen for four different wavelengths in fig 37.7

we have to find the Balmer formula with n and m values of given wavelengths

part(a) Step2: Simplify

Balmer showed that the wavelengths in the hydrogen spectrum could be represented by the simple formula,

where ;m= 1,2,3....

n= any integer greater than m

This formula predicts a series of spectral lines of gradually decreasing wavelength, converging to the series limit wavelength of 364.7 nm as n tends to ∞. This series of spectral lines is now called the Balmer series.

n = any integer greater than m

part(b) Step1: Given information

Balmer series of hydrogen spectrum

We have to find the wavelength for the fifth line of Balmer series spectrum

part(b) Step2 : simplify 

From Balmer formula ,

We know Balmer series starts fromm= 2

So ,the fifth line of Balmer series ism= 2 ton=7

By substituting the value ofm =2and n=7 in Balmer formula ,we get