Quantum and Nuclear Flashcards
How do you find binding energy?
E = mc2 correctly models the relationship between the mass defect and binding energy. Mass defect can be found by calculating the difference between the theoretical mass of a nucleus and the actual mass of a nucleus. Multiplying this value by the speed of light squared will result in the binding energy.
The mass of a proton is 1.0072 amu, while the mass of a neutron is 1.0086 amu. Given that the measured mass of a helium nucleus is 4.0015 amu, how much energy is converted from mass during the formation of one such nucleus? (1 amu = 1.66 x 10-27kg).
First, calculate the mass defect. A helium nucleus has two protons and two neutrons, meaning that the total mass of the protons is 2.0144 amu while that of the neutrons is 2.0172 amu. Combining these values gives a predicted mass of 4.0316 amu. Because the actual mass is 4.0015 amu, the mass defect is roughly 0.030 amu. The next step is to convert the mass to kilograms, the units required for the equation E = mc2. 0.03 amu x (1.66 x 10-27 kg/amu) = 4.98 x 10-29, or about 5 x 10-29, kg. Finally, plug this value in to E = mc2. E = (5 x 10-29 kg) (3 x 108m/s)2 = (4.5 x 10-12 J).
The wavelength of everyday objects is not a useful description in physics. This is because…
The wavelength of an object is calculated using the equation λ = h/mv. As planck’s constant is 6.634 x 10-34, any object with a mass that is not also extremely tiny will result in a wavelength near zero. Values this small are not useful and so are rarely used to describe macroscopic objects.
Consider the mathematical expression of the Heisenberg uncertainty principle. Which of the following correctly explains why the electrons of an atom do NOT come into contact with its positive nucleus? (Note: momentum is defined as the product of a particle’s mass and its velocity).
One useful way to conceptualize Heisenberg’s uncertainty principle is to think of it in terms of the relationship provided in the question stem. The standard deviations of momentum and position are inversely proportional, thus we cannot know the exact momentum or position of a particular electron. If an electron were to come into contact with a proton in the nucleus, its position would be known, implying an infinite increase in its momentum. If this electron had any momentum whatsoever, then it could not stay in one position (e.g. the nucleus).
A scientist is measuring the mass of a uranium nucleus. She finds a value that is almost infinitesimally less than the predicted mass, which she obtained by calculating the total masses of the protons and neutrons in the nucleus. This can most probably be explained by the fact that…
All nuclei weigh less than the sum of their component protons and neutrons, a phenomenon known as mass defect. When subatomic particles come together to form a nucleus some of their mass is converted into energy. Because of the law of conservation of energy, the amount of mass lost can be modeled using Einstein’s famous equation E = mc2.
An electron’s kinetic energy was calculated to be 2.0 x 10-20 J, just after being ejected from an aluminum atom after exposure to high energy photons. Given this information, what was the incident photon’s kinetic energy? (Aluminum’s work function is 8.0 x 10-20 J).
The energy of an ejected electron due to the photoelectric effect is equal to the energy of the incident photon minus the work function of the metal (in this case aluminum). Since we’re asked to find the energy of the photon, the equation arranges to Ephoton = KEelectron + Work function. E = (2.0 x 10-20 J) + (8.0 x 10-20 J). Ephoton = 1 x 10-19 J.
Occurs when two (or more) nuclei are forced together by extremely high levels of energy, causing them to merge to form a new, larger nucleus. The enlarged nucleus has a greater number of protons, which equates to a new (heavier) element.
nuclear fusion
occurs when a larger nucleus is split into two or more smaller nuclei.
Nuclear fission
True or false: the enormous energy released from a fusion reaction is explained by the observation that the product contains lower energy nuclear components compared to the original material.
This statement is false. In order for a fusion reaction to occur, massive amounts of energy must be used to force two atoms together into one. While this process takes a large amount of energy, it releases even more because the new atom is at a lower energy state. The energy released is referred to as the binding energy.
True or False: Gamma radiation involves the emission of an electron
Gamma decay involves the emission of a gamma ray, or high-energy photon, from an excited nucleus. As a gamma ray is a photon, which is massless and has no charge, the atomic number and atomic weight of an atom does not change when it undergoes gamma decay.
A scientist working with radioactive iridium-190 notices that after one hour, there was less than 7% of the sample remaining. How much more time does the scientist have before there is less than 1% of the iridium-190 remaining?
100% = 0 half-lives → 50% = 1 half-life → 25% = 2 half-lives → 12.5% = 3 half-lives → 6.25% = 4 half-lives Thereforem less than 7% Ir-190 corresponds to about 4 half-lives. Since 1 hour has passed: 1 hour / 4 half-lives = 15 mins/half-life 6.25% → 3.125% = 5 half-lives → 1.56% = 6 half-lives → 0.78% = 7 half-lives Therefore, for the sample to be less than 1%, it must have at least 7 half-lives total. (7 - 4 half-lives) x 15 mins/half-life = 3 x 15 = 45 mins = ¾ of an hour
What does the following equation express:
In alpha decay, the atomic nucleus emits an alpha (ɑ) particle, which consists of 2 neutrons and 2 protons. The summary equation for alpha decay can be denoted by the equation.
How would a nuclei vs. time graphs accurately represent the semi-logarithmic plot of exponential decay?
The semi-log plot of radioactive decay transforms the exponential decay graph into a linear plot in which the y-axis is expressed logarithmically, while the x-axis remains unchanged (expressed as time).
the potential energy present in the nucleus of every atom. This potential energy results from the strong nuclear force that holds protons together despite the repulsive force among them that exists due to electromagnetism.
Nuclear binding energy
Albert notes that the actual mass of a copper atom is 1.055 x 10-25 kg. How much of the atom’s mass was converted to 7.637 x 10-12 J of energy upon nuclear formation? (Note that 1 amu = 1.66 x 10-27 kg.)
The amount of mass that is converted into energy (termed nuclear binding energy) during nuclear fusion is known as the mass defect, or the difference between the actual mass of a nucleus and its expected mass. The relationship between binding energy and mass defect is given by Einstein’s surprisingly simple equation: E = mc2, which is to say that energy equals mass times the speed of light squared. Thus, the mass difference can be calculated by isolating m such that: m = E/c2 = 7.637 x 10-12 J / (3.0 x 108 m/s)2 = 8.49 x 10-29 kg. Since 1.66 x 10-27 kg is equivalent to 1 amu, the mass defect of 8.49 x 10-29 kg is equivalent to 0.0511 amu.
If a sample of berkelium-246 undergoes four rounds of alpha decay, what would be the daughter nuclei formed?
Thus, if Bk-246 undergoes four rounds of alpha decay, it would produce:
