Download RAD 107 HOMEWORK 4

RAD 107
HOMEWORK 4
1. A nuclide with mass number A and atomic number Z is denoted by ZA X , where X is the symbol for the
chemical element whose atomic number is Z. For example, the nuclide with A = 11 and Z = 5 is written
11
5 B , because Boron (B) corresponds to Z = 5. Use the Periodic Table (on page 21 of the textbook) to fill out
the table below.
Mass
Number
(A)
11
37
58
98
137
97
126
Atomic
Number
(Z)
5
18
26
42
55
43
53
Nuclide Identifier
11
5
B
Example
2. Because each chemical element corresponds to precisely one value of the atomic number, nuclides can also
be identified by the symbol for the element followed by the mass number (i.e. without also specifying the
atomic number). For example, instead of 146 C we can write C-14 or Carbon-14. Write each of the nuclides
listed in the table above in this way. Example
11
5
B Boron-11.
3. Isotopes are nuclides with the same atomic number (number of protons).
Isobars are nuclides with the same mass number (number of protons + number of neutrons).
Isotones are nuclides with the same number of neutrons.
For the pairs of nuclides listed below, state whether pairs are isotopes, isobars, or isotones
Nuclide Pair
Cs-133, Xe-132
Sn-124, Te-126
Cd-115, Cd-114
Ba-128, Ba-137
Cd-108, Ag-108
O-16, N-16
Mg-25, Al-26
Relationship
(isotopes, isobars,
isotones)
isotones
[Hint. Google this: Table of Nuclides Wikipedia.]
4. Suppose that the energy levels for electrons in Tungsten are
Shell
K
L
M
N
O
P
n
1
2
3
4
5
6
Energy (keV)
-69.5
-12.1
-2.82
-0.59
-0.08
-0.005
where n is the principal quantum number. Fill out the following table.
Shell
Actual Number of
Electrons in Shell of
Tungsten Atom
Max Number of
Electrons in Shell
K
L
M
N
O
P
[Hint: check out page 29 of the textbook.]
5. How much kinetic energy must an electron have in order to knock a Tungsten K-shell electron out a
Tungsten atom? How much to knock out a Tungsten N-shell electron?
[Hint: read the first table in Problem 4.]
6. Suppose that a K-shell electron has been knocked out of a Tungsten atom due to a collision with a fastmoving external electron. If an electron from the L-shell replaces the missing electron in the K-shell,
a) How much energy did the formerly L-shell electron release?
b) What is the frequency of the photon that carried this energy away?
c) Is this photon an x-ray photon? (i.e. is its frequency between 3 x 1016 Hz and 3 x 1019 Hz ?)
[Hint: Use first table of Problem 4. a) EReleased = EInitial - EFinal
defined frequency range for x-rays.]
b) EReleased = hv c) range given is the
7. Repeat Problem 6 for the following electron transitions
Initial Electron
Shell
Final Electron
Shell
M
O
O
P
free
K
L
M
K
K
Energy
Difference
(keV)
[Hint: The energy level of a free electron is 0 keV. ]
Photon
Frequency (Hz)
X-ray?
(Y/N)
8. Plot the principal quantum number n vs. the energy of the associated shell for a Tungsten atom.
[Hint: It will resemble the plot of potential energy of the electron vs. its distance from the nucleus.]
9. An alpha particle is actually the nucleus of a Helium atom. If a nucleus of Uranium-238 undergoes alpha
decay by emitting an alpha particle,
a) What will be the new atomic number of the nucleus?
b) What will be the new mass number?
c) Write down the symbol for the resulting nuclide in the form
[Hint: check out the lecture notes for September 15]
A
Z
X.