The Motor Carrier Permit requires a CA number, issued by the California Highway Patrol (CHP). Contact CHP at (916) 843-4150. In-State Carriers: A commercial vehicle operated only within the state of California must obtain a Motor Carrier Permit, a CA number, and as of September 2016 a U.S. Department of Transportation (DOT) Number as well. See Federal Motor Carrier Safety Administration. In calcium-40, there are 20 neutrons. The number of neutrons can be found with the formula: Number of neutrons = mass number - atomic number Calcium: mass number = 40.08 rArr 40 atomic number = 20 Number of neutrons = relative atomic mass - atomic number Number of neutrons = 40 - 20 Number of neutrons = 20. The atomic mass is useful in chemistry when it is paired with the mole concept: the atomic mass of an element, measured in amu, is the same as the mass in grams of one mole of an element. Thus, since the atomic mass of iron is 55.847 amu, one mole of iron atoms would weigh 55.847 grams. California Public Health Experts: Mass Gatherings Should be Postponed or Canceled Statewide to Slow the Spread of COVID-19 Published: Mar 11, 2020 State public health experts announce that gatherings with 250 people or more should be rescheduled or canceled.

1. Ca Atomic Number Mass Number
2. Mass Number Example

The mass number (symbol A, from the German word Atomgewicht [atomic weight]),^[1] also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It is approximately equal to the atomic (also known as isotopic) mass of the atom expressed in atomic mass units. Since protons and neutrons are both baryons, the mass number A is identical with the baryon numberB of the nucleus (and also of the whole atom or ion). The mass number is different for each different isotope of a chemical element. Hence, the difference between the mass number and the atomic numberZ gives the number of neutrons (N) in a given nucleus: N = A − Z.^[2]

The mass number is written either after the element name or as a superscript to the left of an element's symbol. For example, the most common isotope of carbon is carbon-12, or ¹²
C
, which has 6 protons and 6 neutrons. The full isotope symbol would also have the atomic number (Z) as a subscript to the left of the element symbol directly below the mass number: ¹²
₆C
.^[3]

Mass number changes in radioactive decay[edit]

Ca Atomic Number Mass Number

Different types of radioactive decay are characterized by their changes in mass number as well as atomic number, according to the radioactive displacement law of Fajans and Soddy. For example, uranium-238 usually decays by alpha decay, where the nucleus loses two neutrons and two protons in the form of an alpha particle. Thus the atomic number and the number of neutrons each decrease by 2 (Z: 92 → 90, N: 146 → 144), so that the mass number decreases by 4 (A = 238 → 234); the result is an atom of thorium-234 and an alpha particle (⁴
₂He²⁺
):^[4]

On the other hand, carbon-14 decays by beta decay, whereby one neutron is transmuted into a proton with the emission of an electron and an antineutrino. Thus the atomic number increases by 1 (Z: 6 → 7) and the mass number remains the same (A = 14), while the number of neutrons decreases by 1 (N: 8 → 7).^[5] The resulting atom is nitrogen-14, with seven protons and seven neutrons:

Beta decay is possible because different isobars^[6] have mass differences on the order of a few electron masses. If possible, a nuclide will undergo beta decay to an adjacent isobar with lower mass. In the absence of other decay modes, a cascade of beta decays terminates at the isobar with the lowest atomic mass.

Another type of radioactive decay without change in mass number is emission of a gamma ray from a nuclear isomer or metastable excited state of an atomic nucleus. Since all the protons and neutrons remain in the nucleus unchanged in this process, the mass number is also unchanged.

Mass number and isotopic mass[edit]

The mass number gives an estimate of the isotopic mass measured in atomic mass units (u). For ¹²C, the isotopic mass is exactly 12, since the atomic mass unit is defined as 1/12 of the mass of ¹²C. For other isotopes, the isotopic mass is usually within 0.1 u of the mass number. For example, ³⁵Cl (17 protons and 18 neutrons) has a mass number of 35 and an isotopic mass of 34.96885.^[7] The difference of the actual isotopic mass minus the mass number of an atom is known as the mass excess,^[8] which for ³⁵Cl is –0.03115. Mass excess should not be confused with mass defect which is the difference between the mass of an atom and its constituent particles (namely protons, neutrons and electrons).

There are two reasons for mass excess:

1. The neutron is slightly heavier than the proton. This increases the mass of nuclei with more neutrons than protons relative to the atomic mass unit scale based on ¹²C with equal numbers of protons and neutrons.
2. Nuclear binding energy varies between nuclei. A nucleus with greater binding energy has a lower total energy, and therefore a lower mass according to Einstein's mass–energy equivalence relation E = mc². For ³⁵Cl, the isotopic mass is less than 35, so this must be the dominant factor.

Relative atomic mass of an element[edit]

The mass number should also not be confused with the standard atomic weight (also called atomic weight) of an element, which is the ratio of the average atomic mass of the different isotopes of that element (weighted by abundance) to the unified atomic mass unit.^[9] The atomic weight is an actual mass (made relative, i.e., a ratio), while the mass number is a counted number (and so an integer).

This weighted average can be quite different from the near-integer values for individual isotopic masses. For instance, there are two main isotopes of chlorine: chlorine-35 and chlorine-37. In any given sample of chlorine that has not been subjected to mass separation there will be roughly 75% of chlorine atoms which are chlorine-35 and only 25% of chlorine atoms which are chlorine-37. This gives chlorine a relative atomic mass of 35.5 (actually 35.4527 g/mol).

Moreover, the weighted average mass can be near-integer, but at the same time not corresponding to the mass of any natural isotope. For example, bromine has only two stable isotopes, ⁷⁹Br and ⁸¹Br, naturally present in approximately equal fractions, which leads to the standard atomic mass of bromine close to 80 (79.904 g/mol),^[10] even though the isotope ⁸⁰Br with such mass is unstable.

References[edit]

1. ^Jensen, William B. (2005). The Origins of the Symbols A and Z for Atomic Weight and Number. J. Chem. Educ. 82: 1764. link.
2. ^'How many protons, electrons and neutrons are in an atom of krypton, carbon, oxygen, neon, silver, gold, etc...?'. Thomas Jefferson National Accelerator Facility. Retrieved 2008-08-27.
3. ^'Elemental Notation and Isotopes'. Science Help Online. Archived from the original on 2008-09-13. Retrieved 2008-08-27.
4. ^Suchocki, John. Conceptual Chemistry, 2007. Page 119.
5. ^Curran, Greg (2004). Homework Helpers. Career Press. pp. 78–79. ISBN1-56414-721-5.
6. ^Atoms with the same mass number.
7. ^Wang, M.; Audi, G.; Kondev, F. G.; Huang, W. J.; Naimi, S.; Xu, X. (2017). 'The AME2016 atomic mass evaluation (II). Tables, graphs, and references'(PDF). Chinese Physics C. 41 (3): 030003-1–030003-442. doi:10.1088/1674-1137/41/3/030003.
8. ^'mass excess, Δ'. International Union of Pure and Applied Chemistry. Retrieved 2021-01-13.
9. ^'IUPAC Definition of Relative Atomic Mass'. International Union of Pure and Applied Chemistry. Retrieved 2021-01-13.
10. ^'Atomic Weights and Isotopic Compositions for All Elements'. NIST.

Further reading[edit]

• Bishop, Mark. 'The Structure of Matter and Chemical Elements (ch. 3)'. An Introduction to Chemistry. Chiral Publishing. p. 93. ISBN978-0-9778105-4-3. Retrieved 2008-07-08.

Binding Energy

Thenuclear source of energy is understood only if the concept of binding energy(BE) is understood. The nucleons, as said, are held by short-range nuclearforces. The mass of a nucleus is generally less than the sum of the masses ofthe nucleons. This difference is called the mass-defect.Such a phenomenon is observed in atomic or subatomic levels, and not withordinary materials that we handle, where the total mass has to be the sum of thecomponent masses. The mass-defect is responsible for the binding together of thenucleons. The energy equivalent of the mass-defectis called the binding-energy of the nucleus. Look at the followingillustrative picture and visualize that, when individual nucleons packthemselves together to form a system, which we call nucleus, they liberate someenergy in the form of photons (gamma rays). The liberated energy manifests as areduction in the net mass of the nucleus, as per Einstein’s relation. It mayalso be said that the nucleus could be split intonucleons by supplying external energy equal to the binding energy.

The enormity of the nuclear binding energy can be betterappreciated by comparing it to the binding energy of an electron in an atom. Thenuclear binding energies are on the order of a million times greater than theelectron binding energies of atoms. For example, the bindingenergy of an electron to the nucleus in the hydrogen atom is 13.6 eV,whereas the binding energy ofnucleons in the He-4 nucleus is28,300,000eV (roughly 2 million times!)

BindingEnergy Per Nucleon (BE/A): As the number of particles in a nucleusincreases, the total binding energy also increases. The rate of increase,however, is not uniform. This lack of uniformity results in a variation in theamount of binding energy associated with each nucleon within the nucleus. Thisvariation in the binding energy per nucleon (BE/A) is easily seen when theaverage BE/A is plotted versus atomic mass number (A), as shown in the figurebelow:

Binding Energy per Nucleon vs. Mass Number

Mass Number Example

The above figure illustrates that as theatomic mass number increases, the binding energy per nucleon decreases for A> 60. The BE/A curve reaches a maximum value of 8.79 MeV at A = 56 anddecreases to about 7.6 MeV for A = 238.

The general shape of the BE/A curve can beexplained using the general properties of nuclear forces. As already said, veryshort-range attractive forces that exist between nucleons hold the nucleus inits shape. On the other hand, the long-range repulsive electrostatic (coulomb)forces that exist between all the protons in the nucleus continuously tend toforce the protons apart, thus splitting the nucleus.As the atomic number (Z) increases, therepulsive electrostatic forces within the nucleus increase. To overcome thisincreased repulsion and maintain stability, the proportion of neutrons in thenucleus must increase. This increase in theneutron-to-proton ratio only partially compensates for the growing proton-protonrepulsive force in the heavier, naturally occurring elements. As therepulsive forces are increasing, less energy must be supplied, on the average,to remove a nucleon from the nucleus. In other words, the BE/A has decreased.The BE/A of a nucleus is an indication of its degree of stability.Generally, the more stable nuclides havehigher BE/A than the less stable ones. The increase in the BE/A asthe atomic mass number decreases from 260 to 60 is the primary reason for the energyliberation in the fission process. In addition, the increase in the BE/Aas the atomic mass number increases from 1 to 60 is the reason for the energyliberation in the fusion process, which is the opposite reaction offission.

The heaviest nuclei require only a small energy addition for therelatively large coulomb forces to overcome the attractive nuclear forces, inorder to split the nucleus into two halves. Consequently, the heaviestnuclei are easily fissionable compared to lighter nuclei.The addition of the energy required to cause a distortion in the heavynucleus leading to fission, is commonly achieved by adding a neutron into thenucleus. Some nuclei experience chances of undergoing fission, even withoutadding a neutron, such a phenomenon being called ‘Spontaneous fission’.

In the fusion of Deuterium (a hydrogen isotope H-2)and Tritium (another hydrogen isotope H-3), called the D-T fusion, the totalenergy released is 17.6 MeV. In the fission of U-235 by neutron, the energyreleased is about 200 MeV. Though fission energy seems higher, therelease of energy per unit mass of the fuel, is much higher in the case offusion than in fission.More discussion on fission and fusion will be given later.