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The Bohr Model

Bohr devised Equation 1 to describe the emission spectrum of hydrogen:

In this equation ni is the numerical index of the level of the electron just before it emits light, while nf is the numerical index of the level where the electron winds up after the emission of light. (Note that nf does not necessarily equal 1.) DE is the difference in energy between the two energy levels in question, while RH is a proportionality constant. Since DE is related to the wavelength, l, of light by the equation DE = hc/l, Equation 1 may be written in the equivalent form of Equation 2.

In order to do the algebra required to calculate the value of l for a given transition, it is necessary to know the values of the constants RH, h, and c. They are 2.18 x 10 -18 J, 6.63 x 10-34 J sec, and 3.00 x 108 m/sec, respectively. Substituting these values into Equation 2 produces

For the transition from ni = 6 to nf = 2, DE = - 4.84 x 10-19 J. The negative sign indicates that the energy of the final state is less than that of the initial state. Converting this value of DE into a wavelength yields l = -4.10 x 10 -7 meters or 410 nm. Light of this wavelength is purple. We have ignored the negative sign since the value of l must be positive.

Exercise 1 Calculate the wavelength of the light that is emitted by each of the following electronic transitions in a hydrogen atom. If you use the Rothenberger Calculator, you must enclose each term in the denominator on the right hand side of Equation 2 in parentheses. Here's how you would enter the data for the ni = 6 to nf = 2 transition mentioned above: 9.12/((1/(6*6))-(1/(2*2))). The calculator returns the value -41.04, which is equivalent to 410.4 or 410 nm. Express your answer to 3 significant figures.

ni

nf

l, nm

5

2

4

2

3

2

6

4

2

1

Exercise 2 The electromagnetic spectrum comprises a continuum of wavelengths of radiation. Figure 1 shows the names that scientists have applied to various regions of this spectrum.

What type of radiation does an electron in a hydrogen atom emit when it falls from the

a. n = 6 to n = 4 level?

b. n = 2 to n = 1 level?

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