SCI 270: On Nuclear Technology Practice Problems

## 3. Atoms - the tiny wonders

1. When heated to very high temperature or passing a electric discharge through, a hydrogen gas glows, emitting a purplish light. When analyzed by a prism, the light consists of a few lines with wavelengths listed in the Table.

Wavelength, l Wavenumber, 1/l Frequency, c/l Photon energy, h v n in Balmer series.
nm 106 m-1 1014 Hz 10-19 J Integer
656.3
486.1
434.0
410.1
396.9
389.0

Convert the wavelengths l to wavenumbers and frequencies using the given formulas in multiples and units as indicated. Also evaluate the n in the Balmer series.

2. From the values above, draw a spectrum indicating where the lines will be observed based on a linear frequency scale.

 ```| | | | | |4____________________5____________________6____________________7___________/e14 Hz ```

The Rydberg relationship is usually given in the form as follows:

1
---
l
= - R (1
---
n2
- 1
--- )
4

The Rydberg constant R is ________________________ m-1

However, the Rydberg relationship can be written for frequency (v) as follows:

v = - R (1
---
n2
- 1
--- )
4

The Rydberg constant R is ________________________ Hz

3. The Bohr model and the quantum mechanical approach result in an expression for the Rydberg constant R:

2 p2 m Z2 e4
R = --------------- = 10967700 m-1
c h3

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 (nf = 2, 3, 4, 5, and 6; ni = 1) of the Lyman series.

The formula used:
_____________________________
Wave numbers of the five lines

_____________

_____________

_____________

_____________

_____________

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

_______________________________

4. The characteristic X-rays of some elements are listed here,

Atomic
number
ElementWavelength Frequency Frequency(1/2) Photon energy, h v
nm 1018 Hz 109 Hz(1/2) 10-15 J
23 V 0.2503 1.199
24 Cr 0.2289 1.310
25 Mn 0.2102 1.427
26 Fe 0.1936 1.550
27 Co 0.1789 1.677
28 Ni 0.1657 1.810
29 Cu 0.1541 1.947
30 Zn 0.1435 2.090
42 Mo 0.0746 4.020
47 Ag 0.0559 5.363
79 Au 0.0180 16.650

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.

 ```| | | | | | | | | | | | |______________________________________________________________________ ```

Evaluate the photon energies and plot them against Z2 to see if they fit a straight line.

 ```| | | | | | | | | | | | |______________________________________________________________________ ```

5. Apply the Moseley's law to estimate the wavelength of characteristic X-rays from hydrogen, (H, Z = 1), aluminium (Al, Z = 13), tin (Sn, Z = 50), and uranium (U, Z = 92).

The wavelengths are given below
H Al Sn U

_____________

_____________

_____________

_____________