Calculate the wavelength and predict the color of the first

Edith Mayer

Edith Mayer

Answered question

2022-04-12

Calculate the wavelength and predict the color of the first two lines of the Balmer series for hydrogen. Use the table below.
Wavelength of emission (nm) - Color
400-450 - Violet
450-490 - Blue
490-550 - Green
550-580 - Yellow
580-650 - Orange
650-700 - Red

Answer & Explanation

Eliezer Olson

Eliezer Olson

Beginner2022-04-13Added 16 answers

Here we are asked to calculate the wavelength and to predict the color of the first two lines of the Balmer series for hydrogen.
The wavelength of first two lines of the Balmer series for hydrogen is given as follows
The wavelenght of Balmer series for hydrogen is given by
1 λ = R ( 1 2 2 1 n 2 )
where, λ is wavelength, R is Rydberg constant and n is the energy level from where electron is coming to energy level 2 to make balmer line.
Now, for first Balmer line the value of n is 3 so,
1 λ = R ( 1 2 2 1 3 2 ) 1 λ = R ( 1 4 1 9 ) 1 λ = R ( 9 4 36 ) λ = 36 5 R λ = 36 5 × 1.097 × 10 7 m 1 λ = 36 5.485 × 10 7 λ = 656.335   n m
from the table this wavelength belongs to Red color, hence the first line of balmer series has wavelength 656.335 nm and has Red color.again now, for second Balmer line the value of n is 4 so,
1 λ = R ( 1 2 2 1 4 2 ) 1 λ = R ( 1 4 1 16 ) 1 λ = R ( 4 1 36 ) λ = 16 3 R λ = 16 3 × 1.097 × 10 7 m 1 λ = 486.174   n m
from the table this wavelength belongs to Blue color, hence the second line of balmer series has wavelength 486.174 nm and has Blue color.
Therefore, the wavelength of first two lines of Balmer series for hydrogenare 656.335 nm and 486.174 nm respectively.And the color of first two lines of Balmer series for hydrogen areRed and Blue respectively.

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