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Section summary
The binding energy (BE) of a nucleus is the energy needed to separate it into individual protons and neutrons. In terms of atomic masses,
where
is the mass of a hydrogen atom,
is the atomic mass of the nuclide, and
is the mass of a neutron. Patterns in the binding energy per nucleon,
, reveal details of the nuclear force. The larger the
, the more stable the nucleus.
Conceptual questions
Why is the number of neutrons greater than the number of protons in stable nuclei having
greater than about 40, and why is this effect more pronounced for the heaviest nuclei?
Binding energy is a measure of how much work must be done against nuclear forces in order to disassemble a nucleus into its constituent parts. For example, the amount of energy in order to disassemble
into 2 protons and 2 neutrons requires 28.3 MeV of work to be done on the nuclear particles. Describe the force that makes it so difficult to pull a nucleus apart. Would it be accurate to say that the electric force plays a role in the forces within a nucleus? Explain why or why not.
is a loosely bound isotope of hydrogen. Called deuterium or heavy hydrogen, it is stable but relatively rare—it is 0.015% of natural hydrogen. Note that deuterium has
, which should tend to make it more tightly bound, but both are odd numbers. Calculate
, the binding energy per nucleon, for
and compare it with the approximate value obtained from the graph in
[link] .
is among the most tightly bound of all nuclides. It is more than 90% of natural iron. Note that
has even numbers of both protons and neutrons. Calculate
, the binding energy per nucleon, for
and compare it with the approximate value obtained from the graph in
[link] .
is the heaviest stable nuclide, and its
is low compared with medium-mass nuclides. Calculate
, the binding energy per nucleon, for
and compare it with the approximate value obtained from the graph in
[link] .
(a) Calculate
for
, the rarer of the two most common uranium isotopes. (b) Calculate
for
. (Most of uranium is
.) Note that
has even numbers of both protons and neutrons. Is the
of
significantly different from that of
?
(a) Calculate
for
. Stable and relatively tightly bound, this nuclide is most of natural carbon. (b) Calculate
for
. Is the difference in
between
and
significant? One is stable and common, and the other is unstable and rare.
(a) 7.680 MeV, consistent with graph
(b) 7.520 MeV, consistent with graph. Not significantly different from value for
, but sufficiently lower to allow decay into another nuclide that is more tightly bound.
The fact that
is greatest for
near 60 implies that the range of the nuclear force is about the diameter of such nuclides. (a) Calculate the diameter of an
nucleus. (b) Compare
for
and
. The first is one of the most tightly bound nuclides, while the second is larger and less tightly bound.
The purpose of this problem is to show in three ways that the binding energy of the electron in a hydrogen atom is negligible compared with the masses of the proton and electron. (a) Calculate the mass equivalent in u of the 13.6-eV binding energy of an electron in a hydrogen atom, and compare this with the mass of the hydrogen atom obtained from
[link] . (b) Subtract the mass of the proton given in
[link] from the mass of the hydrogen atom given in
[link] . You will find the difference is equal to the electron’s mass to three digits, implying the binding energy is small in comparison. (c) Take the ratio of the binding energy of the electron (13.6 eV) to the energy equivalent of the electron’s mass (0.511 MeV). (d) Discuss how your answers confirm the stated purpose of this problem.
A particle physicist discovers a neutral particle with a mass of 2.02733 u that he assumes is two neutrons bound together. (a) Find the binding energy. (b) What is unreasonable about this result? (c) What assumptions are unreasonable or inconsistent?
(a)
(b) The negative binding energy implies an unbound system.
(c) This assumption that it is two bound neutrons is incorrect.
Wayne and Dennis like to ride the bike path from Riverside Park to the beach. Dennis’s speed is seven miles per hour faster than Wayne’s speed, so it takes Wayne 2 hours to ride to the beach while it takes Dennis 1.5 hours for the ride. Find the speed of both bikers.
from theory: distance [miles] = speed [mph] × time [hours]
info #1
speed_Dennis × 1.5 = speed_Wayne × 2
=> speed_Wayne = 0.75 × speed_Dennis (i)
info #2
speed_Dennis = speed_Wayne + 7 [mph] (ii)
use (i) in (ii) => [...]
speed_Dennis = 28 mph
speed_Wayne = 21 mph
George
Let W be Wayne's speed in miles per hour and D be Dennis's speed in miles per hour. We know that W + 7 = D and W * 2 = D * 1.5.
Substituting the first equation into the second:
W * 2 = (W + 7) * 1.5
W * 2 = W * 1.5 + 7 * 1.5
0.5 * W = 7 * 1.5
W = 7 * 3 or 21
W is 21
D = W + 7
D = 21 + 7
D = 28
Salma
Devon is 32 32 years older than his son, Milan. The sum of both their ages is 54 54. Using the variables d d and m m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.
please why is it that the 0is in the place of ten thousand
Grace
Send the example to me here and let me see
Stephen
A meditation garden is in the shape of a right triangle, with one leg 7 feet. The length of the hypotenuse is one more than the length of one of the other legs. Find the lengths of the hypotenuse and the other leg
however, may I ask you some questions about Algarba?
Amoon
hi
Enock
what the last part of the problem mean?
Roger
The Jones family took a 15 mile canoe ride down the Indian River in three hours. After lunch, the return trip back up the river took five hours. Find the rate, in mph, of the canoe in still water and the rate of the current.
Shakir works at a computer store. His weekly pay will be either a fixed amount, $925, or $500 plus 12% of his total sales. How much should his total sales be for his variable pay option to exceed the fixed amount of $925.
I'm guessing, but it's somewhere around $4335.00 I think
Lewis
12% of sales will need to exceed 925 - 500, or 425 to exceed fixed amount option. What amount of sales does that equal? 425 ÷ (12÷100) = 3541.67. So the answer is sales greater than 3541.67.
Check:
Sales = 3542
Commission 12%=425.04
Pay = 500 + 425.04 = 925.04.
925.04 > 925.00
Munster
difference between rational and irrational numbers
Jazmine trained for 3 hours on Saturday. She ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. What is her running speed?