SCI 270: On Nuclear Technology Practice Problems |
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Answers are given for your reference only. Please do your part of
the learning, because no one else will be able to do that for you.
Your skills of problem solving are tested and useful in the future. Answers are useless. Acquiring skills and abilities are the goals of learning, marks indications of your performances on these tasks. |
Wavelength l nm | Wavenumber 1/l /10^{6} m^{-1} | Frequency c/l /10^{14} Hz | Photon energy h v /10^{-19} J | n in Balmer series. |
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656.3 | 1.524 | 4.571 | 3.029 | 3 |
486.1 | 2.057 | 6.172 | 4.090 | 4 |
434.0 | 2.304 | 6.912 | 4.580 | 5 |
410.1 | 2.438 | 7.315 | 4.847 | 6 |
396.9 | 2.520 | 7.556 | 5.007 | 7 |
389.0 | 2.570 | 7.712 | 5.110 | 8 |
Convert the wavelengths l to wavenumbers and frequencies using the given formulas and units. Also evaluate the n in the Balmer series (see page 62 of the lecture notes).
I hope the repetitive calculation will let you learn the formulas and theory well.
In order to avoid the repitition of common factors and units, I have used /10^{6} m^{-1} to mean millions per meter.
Unfortunately, some students considered the the factors after the "/" as part of the formula without knowing why and calculate the numbers.
| | | | | | | || | | | | | || |4____________________5____________________6____________________7___________/e14 Hz |
The line spectrum in in e14 Hz are given above. If you have plotted the frequency as a function of 1/n^{2}, we will not mark you wrong.
The Rydberg constant R is | __3.29212e15 Hz__ |
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There are many methods to calculate R. If you use a plot of frequency vs. 1/n^{2} to evaluate it, that is fine. The simplest way is to convert the known value in m^{-1} to Hz by multiplying it by the speed of light or use any two lines to evaluate it.
where m, Z, c, h and e are the mass of the electron, atomic number, speed of light, Planck's constant, and charge of an electron respectively.
Apply this number to calculate the wave numbers of the 5 lines (n_{f} = 2, 3, 4, 5, and 6; n_{i} = 1) of the Lyman series.
The formula used: | wavenumber = -R(1/n^{2} - 1) | |||
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Wave numbers of the five lines | ||||
8.226e6 | 9.750e6 | 10.28e6 | 10.53e6 | 10.66e6 m^{-1} |
You can also plot a spectrum in the UV region for the Lyman series. Having generated these numbers, you have learned how photons are emitted. The energy differences from various energy levels are given out as photons.
In what regions are these lines within the electromagnetic radiation spectrum, visible, UV, IR, Microwave, or X-ray?
These lines are in the region of |
__ Ultraviolet (UV) __ |
Atomic number | Photon energy h v /10^{-15} J | Element | Wavelength nm | Frequency /10^{18} s | Frequency^{(1/2)} /10^{9} |
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23 | 0.794 | V | 0.2503 | 1.199 | 1.095 |
24 | 0.868 | Cr | 0.2289 | 1.310 | 1.145 |
25 | 0.946 | Mn | 0.2102 | 1.427 | 1.195 |
26 | 1.027 | Fe | 0.1936 | 1.550 | 1.245 |
27 | 1.111 | Co | 0.1789 | 1.677 | 1.295 |
28 | 1.199 | Ni | 0.1657 | 1.810 | 1.345 |
29 | 1.290 | Cu | 0.1541 | 1.947 | 1.395 |
30 | 1.385 | Zn | 0.1435 | 2.090 | 1.446 |
42 | 2.664 | Mo | 0.0746 | 4.020 | 2.005 |
47 | 3.554 | Ag | 0.0559 | 5.363 | 2.316 |
79 | 11.03 | Au | 0.0180 | 16.650 | 4.080 |
Complete the Table by taking the square root of the frequencies, and plot
them against the atomic number Z on a graph to see if these data
obey the Moseley's law.
| | | | | | You should get a linear plot | | | | | | |______________________________________________________________________ |
Evaluate the photon energies and plot them against Z^{2}
to see if they fit a straight line.
| | | | | You should get a linear plot | | | | | | | |______________________________________________________________________ |
The wavelengths are given below | |||
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H | Al | Sn | U |
_____________ | _____________ | _____________ | _____________ |
Element, Z | SQRT(f) | Frequency | Wavelength | Wavenumber /m^{-1} |
---|---|---|---|---|
H, 1 | 41924543 | 2.2968e15 | 131 nm | 7.63e6 |
Al, 13 | 6.23e8 | 3.8815e17 | 0.773 nm | 1.29e9 |
Sn, 50 | 2.396e9 | 5.742e18 | 0.0522 nm | 1.92e10 |
U, 92 | 4.409e9 | 1.944e19 | 1.54e-11 m 0.0154 nm | 6.49e10 |
ing on the two points you may choose, the value you estimated may be slightly different. If you used a least-squares line to get the slope, you are doing it properly. Since we do not require math skills here, we choose to use a simple approach in this hint.
Note the wavenumbers for the Lyman series range from 8 to 11 million and the estimate for H here is 7.6 million. Depending on the slope one uses, the agreement can be very good.