**Emission Spectrum of Gases**

**Objectives**

The objective of this experiment is to measure the visible emission spectrum of hydrogen.

**Introduction **

A particular source of radiant energy may emit a single wavelength, as in light from a laser. Radiation composed of a single wavelength is said to be monochromatic. However, most common radiation sources, including light bulbs and stars, produce radiation containing many different wavelengths. When radiation from such sources is separated into its different wavelength components, a **spectrum** is produced. The spectrum so produced consists of a continuous range of colors: Violet merges into blue, blue into green, etc. with no blank spots. This rainbow of colors, containing light of all wavelengths is called a **continuous spectrum**. The most familiar example of a continuous spectrum is the rainbow, produced by the diffraction of sunlight by rain drops.

Not all radiation sources produce a continuous spectrum. When different gases are placed under reduced pressure in a tube and a high voltage is applied, the gases emit different colors of light. The light emitted by neon gas is the familiar red-orange glow of many “neon” lights; sodium vapor emits the yellow light characteristic of some modern streetlights. When light coming from such tubes is passed through a prism, only lines of a few wavelengths are present in the resultant spectra**. **The colored lines are separated by black regions, which correspond to wavelengths that are absent in the light. A spectrum containing radiation of only specific wavelengths is called a **line spectrum**.

When scientists first detected the line spectrum of hydrogen in the mid 1800s, they were fascinated by its simplicity. In 1885 a Swiss schoolteacher named Johann Balmer observed that the frequencies of the four lines of hydrogen fit an intriguingly simple formula:

In this formula C is a constant equal to 3.29 X 10^{15 }s^{-l}. How could the remarkable simplicity of this equation be explained? It took nearly 30 more years to answer this question.

**Bohr’s Model**

After Rutherford’s discovery of the nuclear nature of the atom, scientists thought of the atom as a “microscopic solar system” in which electrons orbited the nucleus. In explaining the line spectrum of hydrogen, Bohr started with this idea, assuming that electrons move in circular orbits around the nucleus. According to classical physics, however, an electrically charged particle (such as an electron) that moves in a circular path should continuously lose energy emitting electromagnetic radiation. As the electron loses energy, it should spiral into the nucleus. Bohr approached this problem in much the same way that Planck had approached the problem of the nature of the radiation emitted by hot objects: He assumed that the prevailing laws of physics were inadequate to describe atoms. Furthermore, he adopted Planck’s idea that energies are quantized. He proposed that only orbits of certain radii, corresponding to certain definite energies, are permitted. An electron in a permitted orbit has a specific energy and is said to be in an “allowed” energy state. An electron in an allowed energy state will not radiate energy and therefore will not spiral into the nucleus.

Using these assumptions, Bohr showed that the electron could circle the nucleus only in orbits of certain specific radii. The allowed orbits have specific energies, given by a simple formula:

E_{n} = (-R_{H})( 1/n^{2}) n = 1, 2, 3, 4, . . .

The constant R_{H} is called the Rydberg constant and has the value of 2.18X10^{-18 }J. The integer n, which can have values from 1 to infinity, is called the principal quantum number. Each orbit corresponds to a different value of n, and the radius of the orbit gets larger as n increases; in fact, the radius is proportional to n^{2}. Thus, the first allowed orbit (the one closest to the nucleus) has n = 1, the next allowed orbit (the one second closest to the nucleus) has n = 2, and so forth. In the lowest energy state, the radius of the electron’s orbit is 52.9 pm. The radius of the orbit for n = 2 is 2^{2} = 4 times larger than the radius of the orbit for n = 1.

The energies of the electron of a hydrogen atom given by the equation above are negative for all values of n. The lower (more negative) the energy is, the more stable the atom will be. The energy is lowest (most negative) for n = 1. As n gets larger; the energy becomes successively less negative and therefore increases. By analogy, a ladder in which the rungs are numbered from the bottom rung on up shows that the higher one climbs the ladder (the greater the value of n), the higher the energy. The lowest energy state (n = 1, analogous to the bottom rung) is called the **ground state** of the atom. When the electron is in a higher energy (less negative) orbit- n ³ 2 or higher-the atom is said to be in an **excited state**.

What happens to the orbit radius and the energy as n becomes infinitely large? The radius increases as n^{2}; we reach a point at which the electron is completely separated from the nucleus. The energy for n = ¥ becomes

E_{} = (-2.18 X 10^{-18 }J)(1/^{2}) = 0

Thus, the state in which the electron is removed from the nucleus is the reference, or zero-energy, state of the hydrogen atom. It is important to remember that this zero-energy state is higher in energy than the states with negative energies.

In order to explain the line spectrum of hydrogen, Bohr made one more startling assumption: He assumed that the electron could “jump” from one allowed energy state to another by absorbing or emitting photons of radiant energy of certain specific frequencies. Energy must be absorbed for an electron to move to a higher energy state (one with a higher value of n). Conversely, radiant energy is emitted when the electron jumps to a lower energy state (one with a lower value of n). The frequency,n, of this radiant energy corresponds exactly to the energy difference between the two states. Thus, if the electron jumps from an initial state with energy E_{i} to a final state with energy E_{f} the following equality will hold:

∆E = E_{f} – E_{i} = h

Bohr’s model of the hydrogen atom therefore states that only the specific frequencies of light that satisfy the equality can be absorbed or emitted by the atom.

To examine a line spectrum a glass tube filled with a gaseous element or compound is attached to a power supply that generates a very large voltage. Exciting electrons in the gas to higher energy levels absorbs energy. When the electrons return to lower energy levels (as they move away from the ionizing beam), light is emitted. Each element has a unique emission spectrum. The emission spectrum may be viewed using a spectra scope (diffraction device).

**Safety **

Care should be taken while handling fragile glass tubes. Remove power before changing gas tubes. Tubes become hot while in use. Let tubes cool on a ceramic square before returning to box.

**Equipment **

- Gas discharge tube power supply
- Helium gas discharge tube
- Hydrogen gas discharge tube
- spectroscope

y

**Procedure**

Calibration of Spectroscope: Although each element always radiates the same emission spectral line pattern, the spectroscope may provide different values from one scope to another. Therefore, the spectroscope must be calibrated with a set of known values.

- Use a helium gas tube with the spectral line values provided below to match to the readings on the spectroscope. Note: spectroscope’s scale is not in nanometers!
- Select a helium gas tube and attach to the power supply.
**DANGER: THE POWER SUPPLY MUST BE OFF WHEN ATTACHING/REMOVING GAS TUBE!** - Turn on the power and use a spectroscope to view the emission spectrum. Record the scale readings in the spaces provided for helium. The violet lines are difficult to read. Attempt to record as many as you can. The more points collected the better the calibration curve. It is possible to achieve excellent results without obtaining all the lines. Use the grouping of colors to help decide how many line(s) per color group.

Here is spectral data that you would observe using the gas discharge tubes looking through a spectroscope |

Graph the Results.

- Plot the actual wavelength on the Y-axis and the scale reading on the X-axis. Make a “best fit” straight-line calibration. See example provided.
- Ensure the power supply is off. Note the tube is hot! Wait for the helium tube to cool before handling. Remove the helium tube and replace with a hydrogen tube.
- Turn on power and take the scale readings for hydrogen’s spectrum. There are four strong lines!
- Record the scale reading from the hydrogen spectrum shown above on the datasheet
- Use the calibration curve to
hydrogen’s scale readings to wavelength in nanometers. Plot the scale reading on the X-axis. Run a vertical line to the calibration line. At the intersection, run a horizontal to the Y-axis. Record the reading on the datasheet.*convert*

Date____________ Name_________________________________________________

**Datasheet**

Helium

Scale reading | ||||||||||||

Wavelength (nm) | 396.4 | 402.6 | 412.0 | 414.4 | 438.7 | 447.1 | 471.3 | 492.2 | 501.6 | 504.8 | 587.6 | 667.8 |

Hydrogen

Scale reading | ||||

Wavelength (nm) |

**Calculations**

- Use the Balmer series to calculate the
**theoretical**wavelength (in nanometers) for hydrogen. Remember that for visible light the final quantum number is 2. Use transitions from n = 6, 5, 4, and 3 to obtain corresponding wavelengths. Then calculate the percent error. Also, provide the energy for a photon from this wavelength.

**1/ = 1.097 X 10 ^{7}m^{-1}(1/n_{f}^{2} – 1/n_{i}^{2})**

Theoretical wavelength from Balmer Series (nm) | ||||

Experimental wavelength | ||||

% ERROR= | ||||

Corresponding ENERGY (kJ) Your data |

EXAMPLE

**HYDROGEN VISIBLE EMISSION SPECTRUM**

**FROM A HELIUM SPECTRUM CALIBRATION**

WAVELENGTH () (**nm**)

He

CALIBRATION CURVE

**CONVERT**

**TO**

**WAVELENGTH**

**(nanometers)**

Data point

**HYDROGEN**

**SCALE**

**READING**

**(no units)**

SPRECTROSCOPE SCALE READING

Date ______ Name ____________________________________________

**Post lab **

- Use the given equation in question 1 to prove that the ionization energy for hydrogen from the
*ground state*is 1312 kJ/mol. - Could you have used an emission spectrum other than helium to calibrate the spectrophotometer?
- What would the absorption spectrum of hydrogen look like? Sketch and label using the diagram below.

Date ______ Name ____________________________________________

**Pre lab **

- Determine the scale reading for each of wavelengths described in the table below, what color would you observe for each wavelength.

Wavelength | Scale reading | Color |

400 nm | ||

500 nm | ||

600 nm | ||

700 nm |

- Answer the following questions
- Use the following equation to calculate the wavelength in meters for the following hydrogen electronic transitions

1/ = 1.097 X 10^{7}m^{-1}(1/n_{f}^{2} – 1/n_{i}^{2})

n=3 to n=1

n=3 to n =2

- Which region of the electromagnetic spectrum would each of these transitions occur?