CK-12-Physics - Intermediate

24.2. The Bohr Atom http://www.ck12.org

FIGURE 24.6

A simple model of a spectroscope.

http://www.youtube.com/watch?v=2tZ6plRHLMg

Hydrogen has only one electron per atom and possesses the simplest line spectrum. The spectrum is shown in detail
in theFigure24.7.

FIGURE 24.7

Hydrogen gas emits line spectra.

Each line is a specific color with a distinct, constant wavelength.

TABLE24.1:

Intensity Color and Position Wavelength

Brightest Red, on right 656 nm

Light blue, in middle 486 nm

Dark blue, on left 434 nm

Faintest Violet, farthest left 410 nm

In 1885, Swiss high-school teacher Johann Balmer (1825-1898) put forth a mathematical description of the line
spectra of the hydrogen atom. He derived an empirical formula that describes the observed wavelengthλfor each
line in the hydrogen spectrum. A different integernis associated with each emission line in theFigure24.7, starting
withn=3 for the red emission line.
1
λ=R

( 1

22 −

1

n^2

)

,n= 3 , 4 ,.. .,

The letterRis known as the Rydberg constant, after Swedish physicist Johannes Robert Rydberg (1854-1919), who
generalized Balmer’s empirical result.

R= 1. 097 × 107 m−^1

Balmer’s equation gives results for emitted hydrogen spectra known today as theBalmer series. See the simulation
below to try the Balmer series.

http://demonstrations.wolfram.com/SpectralSeriesOfTheHydrogenAtom/

Check Your Understanding

1. Show that forn=3, the Balmer series predicts a wavelength of 656 nm.

Answer:

1

λ

=R

(

1

22

−

1

n^2

)

=

1

λ

=R

(

1

22

−

1

32

)

= ( 1. 097 × 107 m−^1 )

(

5

36

)

→

λ= 6. 56 × 10 −^7 m= 656 nm

Could you have predicted thatn=3 corresponded to red light? What happens to the wavelength asngrows larger?

2. Asnincreases, do the spectral lines fall closer together or farther part from one another?

Solution:

528