Post #19-My High School Research Paper
This is my research paper about the spontaneous fission of even-mass rutherfordium and seaborgium isotopes that I wrote for my AP English Literature class in senior year. This got a low B-, because the topic wasn't "debatable". He wrote a comment on my paper that I got a higher score than I deserved, but he acknowledged the good academic-style writing of it. Other students in my class discussed ethical issues and other controversial topics, and some got high A grades. I have always been curious about why the specific isotopes of rutherfordium and seaborgium had such short spontaneous fission half-lives ever since I compiled my first isotope catalog, and so I took advantage of this opportunity to research the origin of the short half-lives. I really wish I could have researched the stabilizing effect of odd amounts of neutrons and/or protons in superheavy nuclei, but I had three other AP classes and I worked 25 hours a week at this point in my life. Here's the paper I wrote, including MLA citations:
Nate
Kloepfer
Mr.
Andrus
AP
English Lit
4
April 2014
Rapid
Spontaneous Fission of Even-Even Rutherfordium and Seaborgium
Isotopes
Looking
at a sequential list of isotopes of the elements rutherfordium and
seaborgium, it is hard for one not to notice the short half-lives of
the isotopes with even amounts of neutrons and protons. For example,
the half-life of even-even rutherfordium-258 is 0.012 seconds, as
compared to the half-lives of rutherfordium-257 and -259, are 4.7
seconds and 2.8 seconds, respectively (“Isotopes of Rutherfordium”
1). The origin of the short half-life of rutherfordium-258, and other
light even-even isotopes of rutherfordium and seaborgium, is their
rapid spontaneous fission. The even-even isotopes of rutherfordium
and seaborgium have comparably short fission half-lives because of
incomplete nucleon shell effects of the two elements, the
destabilizing nature of unpaired nucleons, and the smaller fission
barriers that come with added protons.
One
of the origins of the short spontaneous fission half-lives of
rutherfordium and seaborgium is the incomplete nucleonic shells that
these nuclei have. As a general rule, nuclei with complete nuclear
shells are stabilized more against spontaneous fission than
comparable nuclei with incomplete nuclear shells (Somerville 8). The
dominant nuclear subshells in the rutherfordium-seaborgium region of
nuclear map are neutron numbers N=152 and N=162, and proton numbers
Z=100, Z=102, and Z=108 (“Study of Fission Barriers” 1). The
listed stabilized proton numbers do not include Z=104 (rutherfordium)
or Z=106 (seaborgium), suggesting that Z=104,106 proton number is an
incomplete nuclear subshell that destabilizes the nuclei against
fission.
The
absence of unpaired nucleons in the even-even isotopes of
rutherfordium and seaborgium contributes to their comparably short
spontaneous fission half-lives. The presence of an odd amount of
protons or neutrons increase the fission half-lives by at least one
order of magnitude, and the fission half-lives of odd-odd nuclei
increase by up to 8 orders of magnitude (“Exploring the Island”
1). The reason behind the enhanced stability of nuclei with odd
amounts of nucleons is due to nuclear pairing effects. The absence of
unpaired nucleons in even-even isotopes results in more rapid
spontaneous fission ("The New Isotope 270110"). Like
splitting wood with the grain, paired nucleons in the even-even
isotopes of rutherfordium and seaborgium cause them to fission
easily.
The
primary reason why the even-even isotopes of rutherfordium and
seaborgium have short spontaneous fission half-lives is the presence
of smaller fission barriers. To calculate the fission barriers,
nuclear binding energy is graphed as a function of deformation
(“Study of Fission Barriers” 2). The results of plotting the
fission barriers for even-even superheavy nuclei suggest an overall
lowering of both fission barriers as the proton number increases from
Z=100 to Z=110 (“Study of Fission Barriers” 4). A lower fission
barrier means less resistance to fission, and thus shorter
half-lives. The collapse of the outer, more deformed fission barrier
in the isotopes of rutherfordium destabilize the nuclei to
spontaneous fission. The second fission barrier is nonexistant for
seaborgium isotopes and heavier (Hulet 13). The second fission
barrier is important to the stability of superheavy nuclei, because
it means that the nucleus must undergo a greater deformation to
fission. If a proton-rich nucleus lacks a second fission barrier, the
Coloumb force overwhelms the Strong nuclear force much more easily,
and the nucleus fissions. Thus the rapid fission of rutherfordium and
seaborgium.
The
factors of incomplete subshells, small fission barriers, and the
absence of unpaired nucleons all work together to make the even-even
isotopes of rutherfordium and seaborgium very unstable to spontaneous
fission. The proton subshells of Z=102 and Z=108 mostly confine the
fissioning nuclides to Z=104 (rutherfordium) and Z=106 (seaborgium),
while the decreasing fission barriers of the increasingly proton-rich
nuclei further shortens the half-lives. The instability is confined
to the even-even isotopes of rutherfordium and seaborgium, because of
the absence of unpaired nucleons. Thus the nuclei rutherfordium-254,
256, 258, 260, 262, and seaborgium-258, 260, 262, 264, and 266 all
have dominant fission decay modes with short half-lives.
Works
Cited
Hulet,
E. K. "SciTech Connect:." SciTech
Connect:.
Lawrence Livermore National Laboratory,
n.d.
Web.
Hofmann,
Sigurd, F. Heßberger, and et al. "The new isotope 270110 and
its decay products
266Hs
and 262Sg."link.springer.com.
The European Physical Journal A - Hadrons and Nuclei, n.d. Web. 18
Mar 2014. <link.springer.com/article/10.1007/s10050017013>.
Hofmann,
Sigurd. "Viewpoint: Exploring the island of superheavy
elements." physics.aps.org.
N.p.,
09 Apr 2010. Web. 18 Mar 2014.
<http://physics.aps.org/articles/v3/31?referer=apshome>.
"Isotopes
of Rutherfordium." Wikipedia.
Wikimedia Foundation, 15 Mar. 2014. Web.
Staszczak,
A., J. Dobaczewski, and W. Nazarewicz. "Self-Consistent
Study of Fission Barriers of
Even-Even
Superheavy Nuclei." phys.utk.edu.
PDF.
N.p.: n.p., 2008.
Somerville,
Lawrence P. "Lawrence Berkeley National Laboratory. "Observation
of New
Spontaneous
Fission Activities From Elements 100 To 105 [eScholarship].
N.p., 07 July 2010. Web.
