# Quiz 39: More About Matter Waves

Physics & Astronomy

Q 1Q 1

An electron confined in a one-dimensional infinite potential well has an energy of 180 eV.What is its wavelength?
A)65 pm
B)91 pm
C)130 pm
D)370 pm
E)520 pm

Free

Multiple Choice

B

Q 2Q 2

The ground state energy of an electron in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls is 2.0 eV.If the width of the well is doubled, the ground state energy will be:
A)0.5 eV
B)1.0 eV
C)2.0 eV
D)4.0 eV
E)8.0 eV

Free

Multiple Choice

A

Q 3Q 3

An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls.The ratio E

_{3}/E_{1}of the energy for n = 3 to that for n = 1 is: A)1/3 B)1/9 C)3/1 D)9/1 E)1/1Free

Multiple Choice

D

Q 4Q 4

Identical particles are trapped in one-dimensional wells with infinite potential energy at the walls.The widths L of the traps and the quantum numbers n of the particles are Rank them according to the kinetic energies of the particles, least to greatest.
A)1, 2, 3, 4
B)4, 3, 2, 1
C)1 and 3 tied, then 2, then 4
D)4, then 1 and 3 tied, then 2
E)2, then 1 and 3 tied, then 4

Free

Multiple Choice

Q 5Q 5

Four different particles are trapped in one-dimensional wells with infinite potential energy at their walls.The masses of the particles and the width of the wells are Rank them according to the kinetic energies of the particles when they are in their ground states, lowest to highest.
A)3 and 4 tied, then 2, then 1
B)1, 2, then 3 and 4 tied
C)1 and 2 tied, then 3, then 4
D)4, 3, 2, 1
E)3, 1, 2, 4

Free

Multiple Choice

Q 6Q 6

The ground state energy of an electron in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls:
A)is zero
B)decreases with temperature
C)increases with temperature
D)is independent of temperature
E)oscillates with time

Free

Multiple Choice

Q 7Q 7

Two one-dimensional traps have infinite potential energy at their walls.Trap A has width L and trap B has width 2L.For which value of the quantum number n does a particle in trap B have the same energy as a particle in the ground state of trap A?
A)n = 1
B)n = 2
C)n = 3
D)n = 4
E)n = 5

Free

Multiple Choice

Q 8Q 8

An electron is trapped in a deep well with a width of 0.3 nm.If it is in the state with quantum number n = 3 its kinetic energy is:
A)6.0 10

^{-28}J B)1.8 10^{-27}J C)6.7 10^{-19}J D)2.0 10^{-18}J E)6.0 10^{-18}JFree

Multiple Choice

Q 9Q 9

A particle is trapped in a one-dimensional well with infinite potential energy at the walls.Three possible pairs of energy levels are Order these pairs according to the difference in energy, least to greatest.
A)1, 2, 3
B)3, 2, 1
C)2, 3, 1
D)1, 3, 2
E)3, 1, 2

Free

Multiple Choice

Q 10Q 10

An electron in an atom initially has an energy 5.5 eV above the ground state energy.It drops to a state with energy 3.2 eV above the ground state energy and emits a photon in the process.The wave associated with the photon has a wavelength of:
A)5.4 10

^{}^{7}m B)3.0 10^{}^{7}m C)1.7 10^{}^{7 }m D)1.2 10^{}^{7}m E)1.0 10^{}^{7 }mFree

Multiple Choice

Q 11Q 11

An electron in an atom drops from an energy level at -1.1 10

^{-18}J to an energy level at -2.4 10^{-18}J.The wave associated with the emitted photon has a frequency of: A)2.0 10^{17}Hz B)2.0 10^{15}Hz C)2.0 10^{13}Hz D)2.0 10^{11}Hz E)2.0 10^{9}HzFree

Multiple Choice

Q 12Q 12

An electron in an atom initially has an energy 7.5 eV above the ground state energy.It drops to a state with an energy of 3.2 eV above the ground state energy and emits a photon in the process.The momentum of the photon is:
A)1.7 10

^{-27}kg m/s B)2.3 10^{-27}kg m/s C)4.0 10^{-27}kg m/s D)5.7 10^{-27}kg m/s E)8.0 10^{-27}kg m/sFree

Multiple Choice

Q 13Q 13

An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls.A graph of its wave function (x)versus x is shown.The value of quantum number n is:
A)0
B)1
C)2
D)4
E)8

Free

Multiple Choice

Q 14Q 14

An electron is in a one-dimensional trap with zero potential energy in the interior and infinite potential energy at the walls.A graph of its probability density P(x)versus x is shown.The value of the quantum number n is:
A)0
B)1
C)2
D)3
E)4

Free

Multiple Choice

Q 15Q 15

A particle is trapped in an infinite potential energy well.It is in the state with quantum number n = 14.How many nodes does the probability density have (counting the nodes at the ends of the well)?
A)0
B)7
C)13
D)14
E)15

Free

Multiple Choice

Q 16Q 16

A particle is trapped in an infinite potential energy well.It is in the state with quantum number n = 14.How many maxima does the probability density have?
A)0
B)7
C)13
D)14
E)15

Free

Multiple Choice

Q 17Q 17

A particle is confined to a one-dimensional trap by infinite potential energy walls.Of the following states, designed by the quantum number n, for which one is the probability density greatest near the center of the well?
A)n = 2
B)n = 3
C)n = 4
D)n = 5
E)n = 6

Free

Multiple Choice

Q 18Q 18

If a wave function for a particle moving along the x axis is "normalized" then:
A)

^{2}dt = 1 B)^{2}dx = 1 C)/x = 1 D)/t = 1 E)^{2}= 1Free

Multiple Choice

Q 19Q 19

An electron is in a one-dimensional well with finite potential energy barriers at the walls.The matter wave:
A)is zero at the barriers
B)is zero everywhere within each barrier
C)is zero in the well
D)extends into the barriers
E)is discontinuous at the barriers

Free

Multiple Choice

Q 20Q 20

A particle is confined by finite potential energy walls to a one-dimensional trap from x = 0 to x = L.Its wave function in the region x > L has the form:
A)(x)= A sin(kx)
B)(x)= Ae

^{kx}C)(x)= Ae^{-}^{kx}D)(x)= Ae^{ikx}E)(x)= 0Free

Multiple Choice

Q 21Q 21

A particle in a certain finite potential energy well can have any of five quantized energy values and no more.Which of the following would allow it to have any of six quantized energy levels?
A)Increase the momentum of the particle
B)Decrease the momentum of the particle
C)Decrease the well width
D)Increase the well depth
E)Decrease the well depth

Free

Multiple Choice

Q 22Q 22

A particle is trapped in a finite potential energy well that is deep enough so that the electron can be in the state with n = 4.For this state how many nodes does the probability density have?
A)0
B)1
C)3
D)4
E)5

Free

Multiple Choice

Q 23Q 23

The figure shows the energy levels for an electron in a finite potential energy well.If the electron makes a transition from the n = 3 state to the ground state, what is the wavelength of the emitted photon?
A)6.0 nm
B)5.7 nm
C)5.3 nm
D)3.0 nm
E)2.3 nm

Free

Multiple Choice

Q 24Q 24

The figure shows the energy levels for an electron in a finite potential energy well.If an electron in the n = 2 state absorbs a photon of wavelength 2.0 nm, what happens to the electron?
A)It makes a transition to the n = 3 state.
B)It makes a transition to the n = 4 state.
C)It escapes the well with a kinetic energy of 280 eV.
D)It escapes the well with a kinetic energy of 730 eV.
E)Nothing; this photon does not have an energy corresponding to an allowed transition so it is not absorbed.

Free

Multiple Choice

Q 25Q 25

The quantum number n is most closely associated with what property of the electron in a hydrogen atom?
A)Energy
B)Orbital angular momentum
C)Spin angular momentum
D)Magnetic moment
E)z component of angular momentum

Free

Multiple Choice

Q 26Q 26

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton.Then the ground state energy of a hydrogen atom is -13.6 eV.The minus sign indicates:
A)the kinetic energy is negative
B)the potential energy is positive
C)the electron might escape from the atom
D)the electron and proton are bound together
E)none of the above

Free

Multiple Choice

Q 27Q 27

The wave function for an electron in a state with zero angular momentum:
A)is zero everywhere
B)is spherically symmetric
C)depends on the angle from the z axis
D)depends on the angle from the x axis
E)is spherically symmetric for some shells and depends on the angle from the z axis for others

Free

Multiple Choice

Q 28Q 28

Consider the following: Of these which are spherically symmetric?
A)only I
B)only II
C)only I and II
D)only I and III
E)I, II, and III

Free

Multiple Choice

Q 29Q 29

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton.Then, according to the quantum theory the energy E

_{n}of a state with principal quantum number n is proportional to: A)n B)n^{2}C)1/n D)1/n^{2}E)none of the aboveFree

Multiple Choice

Q 30Q 30

The binding energy of an electron in the ground state in a hydrogen atom is about:
A)1.0 eV
B)3.4 eV
C)10.2 eV
D)13.6 eV
E)27.2 eV

Free

Multiple Choice

Q 31Q 31

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton.Then the ground state energy of a hydrogen atom is -13.6 eV.The energy of the first excited state is:
A)0 eV
B)-3.4 eV
C)-6.8 eV
D)-10.2 eV
E)-27 eV

Free

Multiple Choice

Q 32Q 32

Take the potential energy of a hydrogen atom to be zero for infinite separation of the electron and proton.Then the ground state energy of a hydrogen atom is -13.6 eV.When the electron is in the first excited state its excitation energy (the difference between the energy of the state and that of the ground state)is:
A)0
B)3.4 eV
C)6.8 eV
D)10.2 eV
E)13.6 eV

Free

Multiple Choice

Q 33Q 33

The diagram shows the energy levels for an electron in a certain atom.Of the transitions shown, which represents the emission of a photon with the most energy?
A)I
B)II
C)III
D)IV
E)V

Free

Multiple Choice

Q 34Q 34

When a hydrogen atom makes the transition from the second excited state to the ground state (at -13.6 eV)the energy of the photon emitted is:
A)0 eV
B)1.5 eV
C)9.1 eV
D)12.1 eV
E)13.6 eV

Free

Multiple Choice

Q 35Q 35

The series limit for the Balmer series represents a transition m n, where (m, n)is
A)(2,1)
B)(3,2)
C)(,0)
D)(,1)
E)(,2)

Free

Multiple Choice

Q 36Q 36

The Balmer series of hydrogen is important because it:
A)is the only one for which the Bohr theory can be used
B)is the only series which occurs for hydrogen
C)is in the visible region
D)involves the lowest possible quantum number n
E)involves the highest possible quantum number n

Free

Multiple Choice

Q 37Q 37

Which of the following sets of quantum numbers is possible for an electron in a hydrogen atom?
A)n = 4, ℓ = 3, m

_{ℓ}= −3 B)n = 4, ℓ = 4, m_{ℓ}= −2 C)n = 5, ℓ = −1, m_{ℓ}= 2 D)n = 3, ℓ = 1, m_{ℓ}= −2 E)n = 2, ℓ = 3, m_{ℓ}= −2Free

Multiple Choice

Q 38Q 38

If the wave function is spherically symmetric then the radial probability density is given by:
A)4r

^{2} B)^{2}C)4r^{2}^{2}D)4^{2}E)4r^{2}Free

Multiple Choice

Q 39Q 39

If P(r)is the radial probability density for a hydrogen atom then the probability that the separation of the electron and proton is between r and r + dr is:
A)P dr
B)P

^{2}dr C)4r^{2}P dr D)4r^{2}P dr E)4P drFree

Multiple Choice

Q 40Q 40

The radial probability density for the electron in the ground state of a hydrogen atom has a peak at about:
A)0.5 pm
B)5 pm
C)50 pm
D)500 pm
E)5000 pm

Free

Multiple Choice

Q 41Q 41

The following image is a dot plot of the ground state of the hydrogen atom.The dots represent:
A)all the possible positions of the electron
B)every electron in the atom
C)the electron wave function
D)the volume probability density for the electron
E)the density of the electron cloud

Free

Multiple Choice