can anyone help me with the paraphrase?
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exercise_3_chem_soultion.docx
General Chemistry I - CHEM 181
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Critical Thinking Exercise #3 Due Thursday, Oct. 24 |
Name_________________________ Section _______ |
Why do excited hydrogen atoms emit only specific wavelengths of light?
Introduction
In the 1800’s scientists discovered that a glass cylinder containing a low pressure of a gas will emit light when high voltage electricity is applied to metal electrodes inserted at opposite ends of the cylinder. This principal is used in fluorescent lighting today. When the light emitted by a particular gas, for instance hydrogen, was analyzed by passing it through a prism, scientists were surprised to find that only a few specific wavelengths of visible light were emitted, rather than a continuous range of wavelengths. This mystery took over 70 years to fully solve.
wavelength, (nm)
Infrared
Ultraviolet (uv)
Over time, scientists discovered that the wavelengths of radiation emitted by hydrogen extended from the ultraviolet through the visible into the infrared, microwave, and radio wave portions of the electromagnetic (EM) spectrum. There appeared to be a pattern in the wavelengths that consisted of a series of series of lines. The first 4 series starting from the shortest wavelength line are named for the people that discovered them.
In 1885 J.J. Balmer discovered a mathematical pattern in the wavelengths emitted by hydrogen in the visible and near ultraviolet regions of the electromagnetic spectrum:
Each allowed value for n plugged into this equation produces one of the wavelengths of light emitted by hydrogen in the region of the spectrum that Balmer studied.
Five years later another scientist, Johannes Rydberg, extended this equation so that it could predict all of the wavelengths emitted by hydrogen in all regions of the electromagnetic spectrum:
(eq. 1)
This equation contains two integers that must be greater than zero and the value of n must be greater than the value of m . The way it works is that the value of m specifies the series, e.g. m = 3 is necessary to generate the wavelengths observed in the Paschen series and n = 4,5,6… will generate the wavelengths emitted within that series. The constant R is known as the Rydberg constant.
Though the equations from Balmer and Rydberg demonstrated mathematical skill, they did not answer the big question on the minds of many scientists: Why do the atoms of hydrogen in the gas phase emit only certain wavelengths of radiation and why do the wavelengths have the pattern described by these clever equations. As it turned out, the solution to this riddle completely altered civilization on this planet.
Part I – Putting together pieces of the puzzle
Part of the reason that it took so long to solve hydrogen line spectrum puzzle was that scientists at the time had an incomplete understanding of light. Specifically, they were not aware of any relationship between the energy of light and the wavelength. It was assumed that the energy of light depended entirely on the intensity, which was the square of the amplitude of the light waves according to accepted theory.
This understanding was changed drastically by 1905 due to experiments that revealed that light had a particle nature in addition to its wave nature and that particles of light, which we now call photons, have an energy that is directly proportional to frequency and inversely proportional to the wavelength of the light.
Ephoton = where h is a constant called Plank’s constant
Since , we can also write Eph = (we’ll abbreviate photon as ph)
Step 1: Notice that the left hand side of the Rydberg equation (eq. 1) can easily be converted from into photon energy, Eph, just by multiplying by hc . Naturally, the right hand side of the equation will also need to be multiplied by hc to keeps things equal. Rewrite the Rydberg equation (eq. 1) below in terms of photon energy. The left side of the equation should look like; Eph =
From the equation Ephoton = hc/λ, re-arrange it to get the expression 1/λ.
