Atomic Mass and Exponential Decay

What state is an atom when the atomic number is equal to the number of electrons?

When the atom is neutral.

Isotopes

Atoms of a single element (same atomic number) that differ in number of neutrons in their nuclei (different masses).

Atomic Number

Number of protons in the nucleus.

Mass Number

Combined number of protons and neutrons in the nucleus of an atom.

How to determine the number of neutrons in an atom?

Mass number - atomic number

Hyphen Notation

When the element is listed with the mass number beside it. Ex: carbon-13

Atomic Weight

Measured in amu. The average mass of all the isotopes of an element.

12 amu

Mass of one atom of carbon-12.

Calculating atomic mass

Move percentage over 2 decimal places and multiply by amu. Add values.

Proton mass in amu

1.00728 amu

Neutron mass in amu

1.00866 amu

Mass Defect

Predicted Mass of Nucleus - Actual Mass of Nucleus

Amu to Kg

1 amu = 1.66054 x ,10^-27 kg

How to calculate the energy released when the nucleus is formed from the mass defect?

Using the formula E = mc², convert the mass defect in amus to kg. This will be the mass, then multiply by speed of light squared (2.99792 × 10^8)²

Nuclear Binding Energy

Energy that is released when the nucleus is formed. Also energy needed to break the nucleus apart.

What happens in gamma radiation and how is it connected to E = mc²?

2 particles with noticeable mass disappear and as a result electromagnetic radiation is produced. ER produced can be found from E = mc² due to the conversion of mass to energy.

Strong Force

The force that opposes the electrostatic force between the nucleons of the nucleus, keeping the nucleus stable.

N/Z Ratio

When greater than 1, the atom is unstable. It is the ratio of neutrons to protons.

Alpha decay

Alpha particle is ejected from an unstable nucleus. Charge of an alpha particle is 2+ (has same composition as He nucleus, 2 protons + 2 neutrons).

Beta Decay

An electron is ejected from the nucleus (beta particle). 0 nucleons and -1 charge. A neutron is also converted to a proton (creation of a proton and electron from a neutron).

Gamma Decay

Gamma rays have no charge and no mass. Energy is given off in form of gamma rays, atoms go from their excited states to ground states.

Half-life

Time required for a certain amount of pure substance to reduce to half of its original amount.

Relationship between number of protons and stability

The more protons an atom has, the more unstable. For smaller atoms, proton stability is determined by 1:1 ratio of neutrons to protons.

Formal Charge

Number of valence electrons of isolated atom - ((number of non-binding electrons on bound atom) + (1/2 number of bonding electrons on bound atom)).

What must the sum of all the formal charges on all atoms of a molecule equal?

Net charge of whole molecule.

Fundamental Unit of Charge

e = 1.6 × 10^-19 C

Difference between atomic mass and atomic weight?

The atomic mass is denoted in amu and is nearly equal to the mass number (protons + neutrons mass). Atomic weight is the weighted average of different isotopes of an element.

Why does the mass defect occur?

Result of matter that has been converted to energy.

What force compensates for the repulsion of protons in the nucleus?

Strong nuclear force

What is the mechanism of binding energy?

Bonded nucleons in a system are at a lower energy level than unbounded constituents. The difference in energy must be radiated away.

How does the emission of an alpha particle affect the atomic number and mass number?

The atomic number will be 2 less (-2 protons) and the mass number will be 4 less (-2 protons and -2 neutrons).

What happens in beta decay?

The nucleus is degraded into a proton, beta particle, and antineutrino. Proton is converted to a neutron and beta particle.

Why is beta radiation from radioactive decay more penetrating than alpha radiation?

Electrons are singly charged and much lighter than a proton.

How does beta decay affect the atomic number and mass number?

The atomic number will be 1 less and the mass number does not change.

What is the reverse of beta decay?

Electron capture (atomic number -1).

Avogadro's Number

6.022 × 10²3

Molar Mass of Water

18 g/mol