Physics Final

Question 1

In a double-slit experiment, the maximum intensity of the first bright line on either side of the central one occurs on the screen at locations where the arriving waves differs in path length by

(a) λ/4
(b) λ/2
(c) λ
(d) 2λ

Answer 1

(c) λ

Question 2

Two rays of light from same sources destructively interfere if their path length differ by how much?

Answer 2

l2-l1=(m+1/2)λ

Question 3

In a double-slit experiment it is found that blue light of wavelength 460 nm gives a second-order maximum at a certain location on the screen. What wavelength of visible light would have a minimum at the same location?

Answer 3

For constructive interference
d sinΘ=mλ=2x460nm=920nm
For destructive interference of the other light, we have
d sinΘ=(m’+1/2)λ
When the two angle are equal, then 920nm=(m’+1/2)λ
λ=1.84x103 nm for m’=0 λ=613 nm for m’=1 λ=368 nm for m’=2
The only wavelength here that is visible is 613 nm

Question 4

Visible light includes wavelengths from 4x10-7 m to 7x10-7m. Find the angular width of the first-order spectrum produced by a grating ruled with 800 lines/cm.

Answer 4

The slit space d that corresponding to 800 line/cm is d=(10-2 m/cm)/(8x103 lines/cm)=1.25x10-6 m
Since m=1,
sinΘb=λb/d = 4x10-7m/1.25x10-6m = 0.32, Θb=19o
sinΘr=λr/d = 7x10-7m/1.25x10-6m = 0.56, Θr=34o
The total width of the spectrum is therefore 34o-19o=15o

Question 5

A characteristic property of the spectra produced by a diffraction grating is

(a) the sharpness of the bright lines
(b) diffuseness of the bright lines
(c) absence of bright lines
(d) absence of dark lines

Answer 5

(a) the sharpness of the bright lines

Question 6

The greater the number of lines that are ruled on a grating of given width,

(a) The shorter the wavelengths that can be diffracted
(b) The longer the wavelengths that can be diffracted
(c) The narrower the spectrum that is produced
(d) The broader the spectrum that is produced

Answer 6

(d) The broader the spectrum that is produced

Question 7

White light strikes (a) a diffraction grating, and (b) a prism. A rainbow appears on a screen just below the direction of horizontal incident beam in each case. What is the color of the top of the rainbow in each case?

Answer 7

(a) Violet for diffraction grating (mλ=dsinΘ)

b) Red for prism (n1/n2 = λ2/λ1

Question 8

The theory of relativity is in conflict with

(a) experiment
(b) Newtonian mechanics
(c) electromagnetic theroy
(d) ordinary mathematcs

Answer 8

(b) Newtonian mechanics

Question 9

According to the principle of relativity, the laws of physics are the same in all frames of reference
(a) at rest with respect to one another
(b) moving toward or away from one another
at constant velocity
(c) moving parallel to one another at constant velocity
(d) all of the above

Answer 9

(d) all of the above

Question 10

A young-looking woman astronaut has just arrived home from a long trip. She rushes up to an old gray-haired man and refers him as her son. How might this be possible?

Answer 10

Time dilation: Her clock and biological processes run slowly during her trip since she is moving relative to his rest frame, thus, she returned aged less than he did.

Question 11

If you were on a spaceship traveling at 0.5 c away from a star, at what speed would the starlight pass you?

Answer 11

The speed of light in vacuum is the same by all observers (2nd Principle). You would find that the starlight passes you at c.

Question 12

Find the speed relative to the earth of a spacecraft whose clock runs 1 s slow per day compared to a terrestrial clock.

Answer 12

t=24hx60mim/hx60s/min=86,400 s T=86,401 s
T = t/[1 - (v/c)2]1/2 or
v=c [1 - (t/T)2]1/2 =
=3x108 m/s (1-(86,400 s/86,401 s)2) =1.44x106 m/s

Question 13

If you were traveling away from Earth at speed 0.5 c, would you notice a change in your heartbeat? Would your height and waistline change? What would observers on Earth using telescope say about you?

Answer 13

Since laws of physics are the same for all inertial observers, you would not notice any changes. However, observers on Earth watching you would say your heartbeat is slower, and you are thinner or shorter depending on which dimension of body is in the direction of motion.

Question 14

Suppose the speed of light were infinite. What would you happen to the relativistic predications of length contraction and time dilation?

Answer 14

We would not have to take into account the time light takes to reach us, so none of the relativistic effects would apply, i.e., the relativistic factor (1-(v/c)2)-1/2 would be equal to 1.

Question 15

A spacecraft has left the earth and is moving toward Mars. An observer on the earth finds that, relative to measurements made when it was at rest, the spacecraft’s

(a) length is greater
(b) mass is smaller
(c) clocks tick faster
(d) none of the above

Answer 15

(d) none of the above

Question 16

According to the de Broglie relation, the wavelength of a “matter” wave is inversely proportional to

(a) Planck’s constant.
(b) the frequency of the wave.
(c) the mass of the particle.
(d) the speed of the particle.
(e) the momentum of the particle.

Answer 16

(e) the momentum of the particle.

Question 17

What happens to the de Broglie wavelength of an electron if its momentum is doubled?

(a) The wavelength decreases by a factor of 4.
(b) The wavelength increases by a factor of 2.
(c) The wavelength increases by a factor of 4.
(d) The wavelength decreases by a factor of 2.
(e) The wavelength increases by a factor of 3.

Answer 17

(d) The wavelength decreases by a factor of 2.

Question 18

Determine the de Broglie wavelength of a neutron (m = 1.67 × 10–27 kg) that has a speed of 5.0 m/s.

(a) 79 nm
(b) 395 nm
(c) 1975 nm
(d) 162 nm
(e) 529 nm

Answer 18

(a) 79 nm

Question 19

Upon which one of the following parameters does the energy of a photon depend?

(a) mass
(c) polarization
(e) phase relationships
(b) amplitude
(d) frequency

Answer 19

(d) frequency

Question 20

For which one of the following problems did Max Planck make contributions that eventually led to the development of the “quantum” hypothesis?

(a) photoelectric effect
(b) uncertainty principle
(c) blackbody radiation curves
(d) the motion of the earth in the ether
(e) the invariance of the speed of light through vacuum

Answer 20

(c) blackbody radiation curves

Question 21

Light is usually thought of as wave-like in nature and electrons as particle-like. In which one of the following activities does light behave as a particle or does an electron behave as a wave?

(a) A Young’s double slit experiment is conducted using blue light.
(b) X-rays are used to examine the crystal structure of sodium chloride.
(c) Water is heated to its boiling point in a microwave oven.
(d) An electron enters a parallel plate capacitor and is deflected downward.
(e) A beam of electrons is diffracted as it passes through a narrow slit.

Answer 21

(e) A beam of electrons is diffracted as it passes through a narrow slit.

Question 22

A large value of the probability density Ψ2 of an atomic electron at a certain place and time signifies that the electron

(a) is likely to be found there
(b) is certain to be found there
(c) has a great deal of energy there
(d) has a great deal of charge there

Answer 22

(a) is likely to be found there

Question 23

A moving body is described by the wave function Ψ at a certain time and place. The value of Ψ2 is proportional to the body’s

a. electric field.
b. speed
c. energy
d. probability of being found

Answer 23

d. probability of being found

Question 24

The narrower the wave packet of a particle is
a. the shorter its wavelength
b. the more precisely its position can be
established
c. the more precisely its momentum can be established
d. the more precisely its energy can be established

Answer 24

b. the more precisely its position can be

established

Question 25

The wave packet that corresponds to a moving particle

a. has the same size as the particle
b. has the same speed as the particle
c. has the speed of light
d. consists of x-ray

Answer 25

b. has the same speed as the particle

Question 26

If Planck’s constant were larger than it is,

a. moving bodies would have shorter wavelength
b. moving bodies would have higher energies
c. moving bodies would have higher momenta
d. The uncertainty principle would be significant on a larger scale of size

Answer 26

d. The uncertainty principle would be significant on a larger scale of size

Question 27

If Planck’s constant were changed to 660 J•s, what would be the minimum uncertainty in the position of a 120-kg football player running at a speed of 3.5 m/s?

(a) 0.032 m
(b) 0.13 m
(c) 0.50 m
(d) 0.065 m
(e) 0.25 m

Answer 27

(b) 0.13 m

Question 28

The classical model of the hydrogen atom fails because

(a) a moving electron has more mass than an electron at rest
(b) a moving electron has more charge than an electron at rest
(c) the attractive force of the nucleus is not enough to keep an electron in orbit around it
(d) an accelerated electron radiates electromagnetic waves

Answer 28

(d) an accelerated electron radiates electromagnetic waves

Question 29

In the Bohr model of the hydrogen atom, the electron revolves around the nucleus in order to

(a) emit spectral lines
(b) produce X rays
(c) form energy levels that depend on its speed
(d) keep from falling into the nuclues

Answer 29

(d) keep from falling into the nuclues

Question 30

A hydrogen atom is in its ground state when its orbital electron

(a) is within the nucleus
(b) has escaped from the atom
(c) is in its lowest energy level
(d) is stationary

Answer 30

(c) is in its lowest energy level

Question 31

Find the orbital radius and energy of an electron in a hydrogen atom characterized by principal quantum number n=2.

Answer 31

For n=2, r2=r1n2=0.0529nm(2)2=0.212 nm and

E2=E1/n2=-13.6/22 eV=-3.40 eV

Question 32

With increasing quantum number, the energy difference between adjacent energy levels

(a) decreases
(b) remains the same
(c) increases
(d) sometimes decreases and sometimes increases

Answer 32

(a) decreases

Question 33

An atom emits a photon when one of its electrons

(a) collides with another of its electrons
(b) is removed from the atom
(c) undergoes a transition to a quantum state of lower energy
(d) undergoes a transition to a quantum state of higher energy

Answer 33

(c) undergoes a transition to a quantum state of lower energy

Question 34

The bright-line spectrum produced by the excited atoms of an element contains wavelength that

(a) are the same for all elements
(b) are characteristic of the particular element
(c) are evenly distributed throughout the entire visible spectrum
(d) are different from the wavelength in its dark- line spectrum

Answer 34

(b) are characteristic of the particular element

Question 35

According to the Bohr model, an electron can revolve around the nucleus of a hydrogen indefinitely if its orbit is

(a) a perfect circle
(b) sufficient far from the nucleus to avoid capture
(c) less than one de Broglie wavelength in circumference
(d) exactly one de Broglie wavelength in circumference

Answer 35

(d) exactly one de Broglie wavelength in circumference

Question 36

How can the spectrum of hydrogen contains so many lines when hydrogen contains only one electron?

Answer 36

The electron in the hydrogen atom can be in any of a nearly infinite number of quantized energy levels. A spectral line is emitted when the electron makes a transition from one discrete energy level to another discrete energy of lower energy. A collection of many hydrogen atoms with electrons in different energy levels will give a large number of spectral lines.

Question 37

The quantum theory of the atom

(a) is based on the Bohr theory
(b) is more comprehensive but less accurate than Bohr theory
(c) cannot be reconciled with Newton’s laws of motion
(d) is not based on a mechanical model and considers only observable quantities

Answer 37

(d) is not based on a mechanical model and considers only observable quantities

Question 38

Relative to the sum of the masses of its constituent nucleons, the mass of a nucleus is

a. greater
b. thesame
c. smaller
d. sometimes greater and sometimes smaller

Answer 38

c. smaller

Question 39

The element whose nuclei contains the most tightly bound nucleons is

a. Helium
b. Carbon
c. Iron
d. Uranium

Answer 39

c. Iron

Question 40

Which one of the following statements concerning the magnetic force on a charged particle in a
magnetic field is true?
(a) It is a maximum if the particle is stationary.
(b) It is zero if the particle moves perpendicular to the field. (c) It is a maximum if the particle moves parallel to the field.
(d) It acts in the direction of motion for a positively charged particle.
(e) It depends on the component of the particle’s velocity that is perpendicular to the field.

Answer 40

(e) It depends on the component of the particle’s velocity that is perpendicular to the field.

Question 41

Complete the following statement: The magnitude of the magnetic force that acts on a charged particle in a magnetic field is independent of

(a) the sign of the charge.
(b) the magnitude of the charge.
(c) the magnitude of the magnetic field. (d) the direction of motion of the particle. (e) the velocity components of the particle.

Answer 41

(a) the sign of the charge.

Question 42

A charged particle is moving in a uniform, constant magnetic field. Which one of the following statements concerning the magnetic force exerted on the particle is false?

(a) It does no work on the particle.
(b) It increases the speed of the particle.
(c) It changes the velocity of the particle.
(d) It can act only on a particle in motion.
(e) It does not change the kinetic energy of the particle.

Answer 42

(b) It increases the speed of the particle.

Question 43

Which one of the following statements best explains why a constant magnetic field can do no work on a moving charged particle?

(a) The magnetic field is conservative.
(b) The magnetic force is a velocity dependent force.
(c) The magnetic field is a vector and work is a scalar quantity.
(d) The magnetic force is always perpendicular to the velocity of the particle.
(e) The electric field associated with the particle cancels the effect of the magnetic field on the particle.

Answer 43

(d) The magnetic force is always perpendicular to the velocity of the particle.