<< Chapter < Page Chapter >> Page >
By the end of this section, you will be able to:
  • Describe nuclear structure in terms of protons, neutrons, and electrons
  • Calculate mass defect and binding energy for nuclei
  • Explain trends in the relative stability of nuclei

Nuclear chemistry is the study of reactions that involve changes in nuclear structure. The chapter on atoms, molecules, and ions introduced the basic idea of nuclear structure, that the nucleus of an atom is composed of protons and, with the exception of 1 1 H , neutrons. Recall that the number of protons in the nucleus is called the atomic number (Z) of the element, and the sum of the number of protons and the number of neutrons is the mass number (A). Atoms with the same atomic number but different mass numbers are isotopes of the same element. When referring to a single type of nucleus, we often use the term nuclide    and identify it by the notation Z A X , where X is the symbol for the element, A is the mass number, and Z is the atomic number (for example, 6 14 C ) . Often a nuclide is referenced by the name of the element followed by a hyphen and the mass number. For example, 6 14 C is called “carbon-14.”

Protons and neutrons, collectively called nucleons , are packed together tightly in a nucleus. With a radius of about 10 −15 meters, a nucleus is quite small compared to the radius of the entire atom, which is about 10 −10 meters. Nuclei are extremely dense compared to bulk matter, averaging 1.8 × 10 14 grams per cubic centimeter. For example, water has a density of 1 gram per cubic centimeter, and iridium, one of the densest elements known, has a density of 22.6 g/cm 3 . If the earth’s density were equal to the average nuclear density, the earth’s radius would be only about 200 meters (earth’s actual radius is approximately 6.4 × 10 6 meters, 30,000 times larger). [link] demonstrates just how great nuclear densities can be in the natural world.

Density of a neutron star

Neutron stars form when the core of a very massive star undergoes gravitational collapse, causing the star’s outer layers to explode in a supernova. Composed almost completely of neutrons, they are the densest-known stars in the universe, with densities comparable to the average density of an atomic nucleus. A neutron star in a faraway galaxy has a mass equal to 2.4 solar masses (1 solar mass = M = mass of the sun = 1.99 × 10 30 kg) and a diameter of 26 km.

(a) What is the density of this neutron star?

(b) How does this neutron star’s density compare to the density of a uranium nucleus, which has a diameter of about 15 fm (1 fm = 10 –15 m)?

Solution

We can treat both the neutron star and the U-235 nucleus as spheres. Then the density for both is given by:

d = m V with V = 4 3 π r 3

(a) The radius of the neutron star is 1 2 × 26 km = 1 2 × 2.6 × 10 4 m = 1.3 × 10 4 m , so the density of the neutron star is:

d = m V = m 4 3 π r 3 = 2.4 ( 1.99 × 10 30 kg ) 4 3 π ( 1.3 × 10 4 m ) 3 = 5.2 × 10 17 kg/m 3

(b) The radius of the U-235 nucleus is 1 2 × 15 × 10 −15 m = 7.5 × 10 −15 m , so the density of the U-235 nucleus is:

d = m V = m 4 3 π r 3 = 235 amu ( 1.66 × 10 −27 kg 1 amu ) 4 3 π ( 7.5 × 10 −15 m ) 3 = 2.2 × 10 17 kg/m 3

These values are fairly similar (same order of magnitude), but the nucleus is more than twice as dense as the neutron star.

Check your learning

Find the density of a neutron star with a mass of 1.97 solar masses and a diameter of 13 km, and compare it to the density of a hydrogen nucleus, which has a diameter of 1.75 fm (1 fm = 1 × 10 –15 m).

Answer:

The density of the neutron star is 3.4 × 10 18 kg/m 3 . The density of a hydrogen nucleus is 6.0 × 10 17 kg/m 3 . The neutron star is 5.7 times denser than the hydrogen nucleus.

Got questions? Get instant answers now!

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Ut austin - principles of chemistry. OpenStax CNX. Mar 31, 2016 Download for free at http://legacy.cnx.org/content/col11830/1.13
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Ut austin - principles of chemistry' conversation and receive update notifications?

Ask