the Bohr Model of the hydrogen atom
The Bohr Model describes a hydrogen atom as a postively-charged nucleus which is orbited by a single electron. The electron can only exist in fixed energy orbits, called orbitals.
The differences in energy between orbitals are known as the energy levels of the hydrogen atom.
How can the possible energies of an electron in a hydrogen atom be calculated, according to the Bohr model?
The possible energies (En) of an electron in a hydrogen atom correspond to the formula:
En = -13.6/n2 eV
n is the principal quantum number of the orbital containing the electron.
Note: energy will necessarily be negative for all values of n.
How will energy vary as the value of n increases, according to the Bohr Model?
Energy increases as n increases.
En = -13.6/n2 eV
En is the energy of between nucleus and electron and will always be negative.Since n appears in the denominator, increasing n corresponds to the energy becoming less negative or more positive.
What is the equation for energy difference of an electron as it changes from an orbital with principal quantum number ni (initial) to nf (final), according to the Bohr Model?
The energy difference is:
ΔE = -13.6(1/nf2-1/ni2) eV
This shortcuts having to apply the Bohr Model energy formula to both orbitals and then subtract the initial energy from the final energy.
How much has energy increased, if an electron jumps from n=1 to n=2?
From ΔE = -13.6(1/nf2-1/ni2) eV
nf = 2, ni = 1, giving
ΔE = -13.6(1/22-1/12)
= -13.6(1/4 -1) = -13.6(-3/4)
= 10.2 eV
the emission spectrum of a hydrogen atom
Hydrogen's emission spectrum is the set of frequencies of light that a hydrogen atom can emit.
These particular frequencies are constant, and are uniquely characteristic of hydrogen.
Every element has a distinct emission spectrum; the presence of an element can be proven by observing its unique spectral lines.
How does the Bohr Model explain the frequency of the spectral lines in the emission spectrum of hydrogen?
Each emission spectral line is a result of the difference in energies between orbitals in the Bohr Model.
When an electron in a higher energy orbital falls into a lower energy orbital, it releases energy in the form of a photon. The frequency of the photon is determined by the difference in energy levels of the two orbitals. A large energy difference results in a higher photon frequency.
What are the characteristics of a proton?
A proton is a positively-charged subatomic particle.
Protons have mass of 1 AMU.
A proton is found inside the nucleus of an atom.
Protons contribute to the atomic mass and the atomic number.
What are the characteristics of a neutron?
A neutron is an uncharged subatomic particle.
Neutrons have mass of 1 AMU.
A neutron is found inside the nucleus of an atom.
Neutrons contribute to the atomic mass, but not the atomic number.
the atomic mass, A, of an atom
An atom's atomic mass corresponds to the sum of the neutrons and protons contained in the nucleus of that element.
The units of atomic mass are atomic mass units, AMU.
Force is the change in velocity per unit time that a given mass is experiencing. Force can also be thought of as the change in momentum per unit time.
The SI unit of force is the Newton (N),
1N = 1 kg*m/s2
What must be done to momentum, for an object to suddenly experience twice as much force on it?
Momentum per unit time must be doubled.
Since force is the change in momentum per unit time, these are directly proportional.
Describe Newton's first law of motion.
aka the Law of Inertia: An object in motion will continue with constant velocity unless acted on by a net force.
Similarly, an object at rest will continue to remain at rest until acted on by a net force.
What must be true about the acceleration of an object, if all forces acting on it cancel?
The object has zero acceleration.
Since all forces cancel to be zero, there is not a net force and there will not be a change in velocity. If there is no change in velocity, that is the same as no acceleration.
What is the relationship between force, mass, and acceleration in Newton's second law of motion?
Fnet = ma
Note: net force and acceleration are both vectors, and must be pointing in the same direction.
What is the proportional change in force to make an object move with twice its original acceleration?
Twice the original force must be applied.
From Newton's second law, F=ma. Force and acceleration are directly proportional.
How does Newton's third law of motion describe the forces between two objects?
F1on2 = -F2on1
For every force from one object on a second, there is an equal and opposite force from the second back on the first.
What magnitude of force must exist from apple to an orange in free space, if it's found that there is a force from the orange to the apple of 5N.
From Newton's third law, every force excerted must have an equal and opposite force. The negative sign is already factored in, since the question specified direction.
What is the formula for gravitational force?
Fg = Gm1m2 / r2
G = gravitational constant in N*m2/kg2
m1 and m2 = masses in kg
r = distance between masses in m
What SI unit and common variables are associated with length?
Length or distance has SI units of meters (m).
The variable d and x are used for distance, h for height, z for depth, and r for radius.
What SI unit and common variables are associated with time?
Time has SI units of seconds (s).
The variable t is used for time, T is used for period and also has SI units of seconds.
What SI unit and common variables are associated with area?
Area has SI units of meters2 (m2).
The variable A is used for area, S is used for surface area.
What SI unit and common variables are associated with volume?
Volume has SI units of meters3 (m3).
The variable V is used for volume.
What SI unit and common variables are associated with velocity?
Velocity or speed has SI units of meters/seconds (m/s).
The variable v is used for velocity (a vector), though rarely used, s may be used for speed (magnitude only, scalar).
What SI unit and common variables are associated with acceleration?
Acceleration has SI units of meters/seconds2 (m/s2).
The variable a is used for acceleration (a vector).
What two characteristics are necessary to define a vector?
Magnitude and direction.
magnitude of a vector
Magnitude is the quantity, size, or amount and is a scalar value since it lacks direction.
direction of a vector
Direction provides spacial orientation, angle, or path.
By convention, two perpendicular directions are fixed as positive (right and up) and their opposites as negative (left and down).