Examples of average atomic mass in the following topics:
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- The average atomic mass of an element is the sum of the masses of its isotopes, each multiplied by its natural abundance.
- To calculate the average atomic mass, multiply the fraction by the mass number for each isotope, then add them together.
- Average atomic mass of chlorine = (0.7577 $\cdot$ 35 amu) + (0.2423 $\cdot$ 37 amu) = 35.48 amu
- Average atomic mass of boron = (0.199
$\cdot$
10 amu) + (0.801
$\cdot$
11 amu) = 10.80 amu
- Calculate the average atomic mass of an element given its isotopes and their natural abundance
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- Protons and neutrons both weigh about one atomic mass unit or amu.
- Scientists determine the atomic mass by calculating the mean of the mass numbers for its naturally-occurring isotopes.
- For example, the atomic mass of chlorine (Cl) is 35.45 amu because chlorine is composed of several isotopes, some (the majority) with an atomic mass of 35 amu (17 protons and 18 neutrons) and some with an atomic mass of 37 amu (17 protons and 20 neutrons).
- Its average atomic mass is 12.11.
- Determine the relationship between the mass number of an atom, its atomic number, its atomic mass, and its number of subatomic particles
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- The relative atomic mass is a ratio between the average mass of an element and 1/12 of the mass of an atom of carbon-12.
- From the relative atomic mass of each element, it is possible to determine each element's molar mass by multiplying the molar mass constant (1 g/mol) by the atomic weight of that particular element.
- Multiplying by the molar mass constant ensures that the calculation is dimensionally correct because atomic weights are dimensionless.
- For a single element, the molar mass is equivalent to its atomic weight multiplied by the molar mass constant (1 g/mol).
- For a compound, the molar mass is the sum of the atomic weights of each element in the compound multiplied by the molar mass constant.
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- The position of COM is mass weighted average of the positions of particles.
- In the previous atom on "Center of Mass and Translational Motion," we learned why the concept of center of mass (COM) helps solving mechanics problems involving a rigid body.
- The center of mass is a statement of spatial arrangement of mass (i.e. distribution of mass within the system).
- This mean means that position of COM is mass weighted average of the positions of particles.
- Identify the center of mass for an object with continuous mass distribution
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- Nuclear binding energy accounts for a noticeable difference between the actual mass of an atom's nucleus and its expected mass based on the sum of the masses of its non-bound components.
- Mass defect (Md) can be calculated as the difference between observed atomic mass (mo) and that expected from the combined masses of its protons (mp, each proton having a mass of 1.00728 amu) and neutrons (mn, 1.00867 amu):
- Calculate the average binding energy per mole of a U-235 isotope.
- $2.7843\times10^{-10}\frac{Joules}{atom}\ \times \frac {6.02\times10^{23}\ atoms}{mole}\times \frac{1\ kJ}{1000\ joules} =$ 1.6762 x 1011$\frac{kJ}{mole}$
- Calculate the mass defect and nuclear binding energy of an atom
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- The mass of one mole of atoms of a pure element in grams is equivalent to the atomic mass of that element in atomic mass units (amu) or in grams per mole (g/mol).
- The characteristic molar mass of an element is simply the atomic mass in g/mol.
- However, molar mass can also be calculated by multiplying the atomic mass in amu by the molar mass constant (1 g/mol).
- To calculate the molar mass of a compound with multiple atoms, sum all the atomic mass of the constituent atoms.
- For example, the molar mass of NaCl can be calculated for finding the atomic mass of sodium (22.99 g/mol) and the atomic mass of chlorine (35.45 g/mol) and combining them.
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- Also, the temperature of an ideal monatomic gas is a measure of the average kinetic energy of its atoms, as illustrated in .
- where m is the particle mass and v its speed (the magnitude of its velocity).
- In kinetic theory, the temperature of a classical ideal gas is related to its average kinetic energy per degree of freedom Ek via the equation:
- We will derive this relationship in the following atoms.
- Here, the size of helium atoms relative to their spacing is shown to scale under 1950 atmospheres of pressure.
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- Atoms are made up of particles called protons, neutrons, and electrons, which are responsible for the mass and charge of atoms.
- This can be determined using the atomic number and the mass number of the element (see the concept on atomic numbers and mass numbers).
- Scientists define this amount of mass as one atomic mass unit (amu) or one Dalton.
- Electrons are much smaller in mass than protons, weighing only 9.11 × 10-28 grams, or about 1/1800 of an atomic mass unit.
- When considering atomic mass, it is customary to ignore the mass of any electrons and calculate the atom's mass based on the number of protons and neutrons alone.
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- From the perspective of quantum theory, light is made of photons: particles with zero mass but which carry energy and – importantly in this argument – momentum.
- According to special relativity, because photons are devoid of mass, their energy (E) and momentum (p) are related by E=pc.
- If the absorption and emission are repeated many times, the average speed (and therefore the kinetic energy) of the atom will be reduced.
- Since the temperature of a group of atoms is a measure of the average random internal kinetic energy, this is equivalent to cooling the atoms.
- Atoms are slowed down by absorbing (and emitting) photons.
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- Consider a gas of N molecules, each of mass m, enclosed in a cubical container of volume V=L3.
- where the bar denotes an average over the N particles.
- Pressure arises from the force exerted by molecules or atoms impacting on the walls of a container.
- Here, the size of helium atoms relative to their spacing is shown to scale under 1950 atmospheres of pressure.
- Express the relationship between the pressure and the average kinetic energy of gas molecules in the form of equation