**Johan Rydberg(1854-1919)**

**As a Swedish mathematician, Rydberg analyzed many atomic
spectra in an attempt to understand the periodic system of the elements. He
eventually developed what has become known as the Rydberg Equation.** **Although
nominated, the Nobel prize was never awarded to Rydberg. ****( Please note that these sample calculations are done in
Angstroms and the Rydberg constant is given in units of 1/meters.
The Brady text gives the constant in 1/centimeters.) **

When white light passes through a prism, it is separated into components (visible

Heating hydrogen and passing the light through a prism gives
the following spectrum:

Consider the excitation of hydrogen's electron from the ground
state (n=1) to the 5^{th} shell (n=5).

The **blue line** results when
the electron returns directly from n=5 to n=2.

**Rydberg
developed the following equation to fit hydrogen's atomic spectrum:**

**R
= Rydberg constant = 1.0974x10 ^{7}
m^{-1}**

**To express Rydberg equation in angstroms:**

**1/l = [1.0974x10 ^{7}m^{-1}][1/n_{1}^{2}
- 1/n_{2}^{2}]**

**Practice Problems**

** **

**Problem #1**

Use Rydberg equation to calculate wavelength when electron
returns from n=5 to n=2.

911A/**l** = [1/n_{1}^{2}
- 1/n_{2}^{2}]

911A/**l** = [1/2^{2}
- 1/5^{2}] = 0.25 - 0.0400
= 0.21

**l** = 911A/0.21 = **4340A
Blue**

**Problem #2**

For** ****l**
= 10,900A, use Rydberg equation to determine initial and final energy levels.

911A/**l** = [1/n_{1}^{2}
- 1/n_{2}^{2}]

911A/10900A = 0.0836 = DIF

DIF = [1/n_{1}^{2}
- 1/n_{2}^{2}] = **0.0836**
check table for the best fit!

The best fit involves n=6 to n=3

[1/3^{2} -
1/6^{2}] = 0.111- 0.0278 =
**0.0832**

__Problem #3__

One electron de-excites from n = 8 to n =2. Another electron
de-excites from n = 2 to n = 1.

Which emits the greater energy? Explain!

For n = 8 to n = 2:
For n = 2 to n = 1:

911A/**l** = [1/2^{2} -
1/8^{2}]
911A/**l** = [1/1^{2} - 1/2^{2}]

= 0.25 - 0.0156 = 0.234
= 1.00 - 0.25 = 0.75

= 911A/0.234 = 3890A
**= 911A/0.75 =**
**1215A**

**(shorter l
higher energy)**