MCAT Physics Crash Course

Question 1

Define:

the Bohr Model of the hydrogen atom

Answer 1

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.

Question 2

How can the possible energies of an electron in a hydrogen atom be calculated, according to the Bohr model?

Answer 2

The possible energies (E_n) of an electron in a hydrogen atom correspond to the formula:

E_n = -13.6/n² eV

Where:

n is the principal quantum number of the orbital containing the electron.

Note: energy will necessarily be negative for all values of n.

Question 3

How will energy vary as the value of n increases, according to the Bohr Model?

Answer 3

Energy increases as n increases.

E_n = -13.6/n² eV

E_n 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.

Question 4

What is the equation for energy difference of an electron as it changes from an orbital with principal quantum number n_i (initial) to n_f (final), according to the Bohr Model?

Answer 4

The energy difference is:

ΔE = -13.6(1/n_f²-1/n_i²) eV

This shortcuts having to apply the Bohr Model energy formula to both orbitals and then subtract the initial energy from the final energy.

Question 5

How much has energy increased, if an electron jumps from n=1 to n=2?

Answer 5

10.2 eV

From ΔE = -13.6(1/n_f²-1/n_i²) eV

n_f = 2, n_i = 1, giving
ΔE = -13.6(1/2²-1/1²)
= -13.6(1/4 -1) = -13.6(-3/4)
= 10.2 eV

Question 6

Define:

the emission spectrum of a hydrogen atom

Answer 6

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.

Question 7

How does the Bohr Model explain the frequency of the spectral lines in the emission spectrum of hydrogen?

Answer 7

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.

Question 8

What are the characteristics of a proton?

Answer 8

• 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.

Question 9

What are the characteristics of a neutron?

Answer 9

• 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.

Question 10

Define:

the atomic mass, A, of an atom

Answer 10

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.

Question 11

Define and give units for:

Force

Answer 11

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

Question 12

What must be done to momentum, for an object to suddenly experience twice as much force on it?

Answer 12

Momentum per unit time must be doubled.

Since force is the change in momentum per unit time, these are directly proportional.

Question 13

Describe Newton’s first law of motion.

Answer 13

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.

Question 14

What must be true about the acceleration of an object, if all forces acting on it cancel?

Answer 14

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.

Question 15

What is the relationship between force, mass, and acceleration in Newton’s second law of motion?

Answer 15

F_net = ma

Note: net force and acceleration are both vectors, and must be pointing in the same direction.

Question 16

What is the proportional change in force to make an object move with twice its original acceleration?

Answer 16

Twice the original force must be applied.

From Newton’s second law, F=ma. Force and acceleration are directly proportional.

Question 17

How does Newton’s third law of motion describe the forces between two objects?

Answer 17

F_1on2 = -F_2on1

For every force from one object on a second, there is an equal and opposite force from the second back on the first.

Question 18

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.

Answer 18

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.

Question 19

What is the formula for gravitational force?

Answer 19

F_g = Gm₁m₂ / r²

Where:

G = gravitational constant in N*m²/kg²
m₁ and m₂ = masses in kg
r = distance between masses in m

Question 20

What SI unit and common variables are associated with length?

Answer 20

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.

Question 21

What SI unit and common variables are associated with time?

Answer 21

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.

Question 22

What SI unit and common variables are associated with area?

Answer 22

Area has SI units of meters^<b>2</b>(m²).

The variable A is used for area, S is used for surface area.

Question 23

What SI unit and common variables are associated with volume?

Answer 23

Volume has SI units of meters³(m³).

The variable V is used for volume.

Question 24

What SI unit and common variables are associated with velocity?

Answer 24

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).

Question 25

What SI unit and common variables are associated with **acceleration**?

Answer 25

**Acceleration** has SI units of **meters/seconds² ****(m/s²).** ## Footnote The variable a is used for acceleration (a vector).

Question 26

What two characteristics are necessary to define a **vector**?

Answer 26

**Magnitude** and **direction**.

Question 27

# Define: **magnitude** of a vector

Answer 27

**Magnitude **is the quantity, size, or amount and is a scalar value since it lacks direction.

Question 28

# Define: **direction** of a vector

Answer 28

**Direction** provides spacial orientation, angle, or path. ## Footnote By convention, two perpendicular directions are fixed as positive (right and up) and their opposites as negative (left and down).