Question 1

An electron is confined in a one-dimensional box (an infinite well). Two adjacent allowed energies of the electron are 1.068 × 10-18 J and 1.352 × 10-18 J. What is the length of the box? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg)

Accepted Answer

A)  1.9 nm 
B)  0.93 nm 
C)  1.1 nm 
D)  2.3 nm

Question 2

An electron is in an infinite square well that is 2.6 nm wide. What is the smallest value of the state quantum number n for which the energy level exceeds 100 eV? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg, 1 eV = 1.60 × 10-19)

Accepted Answer

A)  43 
B)  44 
C)  45 
D)  42 
E)  41

Question 3

Calculate the kinetic energy (in eV) of a nonrelativistic neutron that has a de Broglie wavelength of 9.9 × 10^-12 m. (h = 6.626 × 10^-34 J ∙ s, m_neutron = 1.675 × 10^-27 kg, 1 eV = 1.60 10^-19 J)

Accepted Answer

The answer of Calculate the kinetic energy (in eV) of...

Question 4

A laser emits light of wavelength 463 nm during a brief pulse that lasts for 25 ms and has a total energy of 1.2 J. How many photons are emitted in that single pulse? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s)

Accepted Answer

A)  2.8 × 1018 
B)  6.9 × 1019 
C)  3.4 × 1019 
D)  1.1 × 1017 
E)  2.2 × 1017

Question 5

A hydrogen atom makes a downward transition from the n = 20 state to the n = 5 state. Find the wavelength of the emitted photon. The lowest level energy state of hydrogen is -13.6 eV.
(h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J, c = 3.00 × 108 m/s)

Accepted Answer

A)  2.43 μm 
B)  1.46 μm 
C)  1.94 μm 
D)  2.92 μm

Question 6

A metal surface has a work function of 1.50 eV. Calculate the maximum kinetic energy, in eV, of electrons ejected from this surface by electromagnetic radiation of wavelength 311 nm. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, e = - 1.60 × 10^-19 C, 1 eV = 1.60 × 10^-19 J)

Accepted Answer

The answer of A metal surface has a work function...

Question 7

How fast must a nonrelativistic electron move so its de Broglie wavelength is the same as the wavelength of a 3.4-eV photon? (mel = 9.11 × 10-31 kg, c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J)

Accepted Answer

A)  2000 m/s 
B)  1900 m/s 
C)  1700 m/s 
D)  1600 m/s 
E)  1400 m/s

Question 8

What is the orbital radius of the n = 3 excited state in the Bohr model of the hydrogen atom? The ground-state radius of the hydrogen atom is 0.529 × 10-10 m.

Accepted Answer

A)  0.476 nm 
B)  0.159 nm 
C)  0.381 nm 
D)  0.548 nm

Question 9

A metal having a work function of 2.4 eV is illuminated with monochromatic light whose photon energy is 4.0 eV. What is the maximum kinetic energy of the photoelectrons produced by this light? (h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J)

Accepted Answer

A)  2.6 × 10-19 J 
B)  3.8 × 10-19 J 
C)  4.7 × 10-19 J 
D)  5.5 × 10-19 J 
E)  6.4 × 10-19 J

Question 10

You want to have an electron in an energy level where its speed is no more than 66 m/s. What is the length of the smallest box (an infinite well) in which you can do this? (h = 6.626 × 10-34 J ∙ s,
Mel = 9.11 × 10-31 kg)

Accepted Answer

A)  5.5 µm 
B)  11 µm 
C)  2.8 µm 
D)  1.4 µm

Question 11

When a certain metal is illuminated by light, photoelectrons are observed provided that the wavelength of the light is less than 669 nm. Which one of the following values is closest to the work function of this metal? (h = 6.626 × 10-34 J ∙ s, c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J)

Accepted Answer

A)  1.9 eV 
B)  2.0 eV 
C)  2.2 eV 
D)  2.3 eV

Question 12

The Bohr radius of the hydrogen atom is 0.529 × 10-10 m. What is the radius of the n = 2 state?

Accepted Answer

A)  1.06 × 10-10 m 
B)  2.12 × 10-10 m 
C)  0.265 × 10-10 m 
D)  0.529 × 10-10 m 
E)  4.23 × 10-10 m

Question 13

An electron is in an infinite square well (a box) that is 8.9 nm wide. What is the ground state energy of the electron? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg, 1 eV = 1.60 × 10-19)

Accepted Answer

A)  0.0048 eV 
B)  0.0057 eV 
C)  0.0066 eV 
D)  0.0076 eV 
E)  0.0085 eV

Question 14

When a metal surface is illuminated with light of wavelength 437 nm, the stopping potential for photoelectrons is 1.67 V. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, e = - 1.60 × 10^-19 C, 1 eV = 1.60 × 10^-19 J, m_el = 9.11 × 10^-31 kg) (a) What is the work function of the metal, in eV? (b) What is the maximum speed of the ejected electrons?

Accepted Answer

The answer of When a metal surface is illuminated with...

Question 15

A nonrelativistic electron is accelerated from rest through a potential difference. After acceleration the electron has a de Broglie wavelength of 880 nm. What is the potential difference though which this electron was accelerated? (h = 6.626 × 10-34 J ∙ s, e = - 1.60 × 10-19 C, mel = 9.11 × 10-31 kg)

Accepted Answer

A)  1.9 µV 
B)  1.7 µV 
C)  2.2 µV 
D)  2.5 µV

Question 16

Suppose that in a parallel universe, the proton and electron were identical to their counterparts in our own universe EXCEPT that the electron had twice as much charge as our electron. In our present universe, the radius of the first Bohr orbit for hydrogen is a₀ and the speed of an electron in that orbit is v₀. In the parallel universe (a) what would be the radius (in terms of a₀) of the first Bohr orbit for hydrogen? (b) what would be the speed (in terms of v₀) of an electron in the first Bohr orbit for hydrogen?

Accepted Answer

The answer of Suppose that in a parallel universe, the...

Question 17

An 84-kW AM radio station broadcasts at 1000 kHz . How many photons are emitted each second by the transmitting antenna? (h = 6.626 × 10-34 J ∙ s)

Accepted Answer

A)  1.3 × 1032 
B)  2.9 × 1024 
C)  6.3 × 1012 
D)  1.4 × 1015

Question 18

A gas of helium atoms (each of mass 6.65 × 10-27 kg) are at room temperature of 20.0°C. What is the de Broglie wavelength of the helium atoms that are moving at the root-mean-square speed? (h = 6.626 × 10-34 J ∙ s, the Boltzmann constant is 1.38 × 10-23 J/K)

Accepted Answer

A)  5.22 × 10-11 m 
B)  7.38 × 10-11 m 
C)  1.04 × 10-10 m 
D)  2.82 × 10-10 m 
E)  3.99 × 10-10 m

Question 19

An electron in an infinite potential well (a box) makes a transition from the n = 3 level to the ground state and in so doing emits a photon of wavelength 20.9 nm. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34J ∙ s, m_el = 9.11 × 10^-31 kg) (a) What is the width of this well? (b) What wavelength photon would be required to excite the electron from its original level to the next higher one?

Accepted Answer

The answer of An electron in an infinite potential well...

Question 20

An electron is bound in an infinite square-well potential (a box) on the x-axis. The width of the well is L and the well extends from x = 0.00 nm to  In its present state, the normalized wave function of the electron is given by: ψ(x) = 
  
Sin (2πx/L). What is the energy of the electron in this state?(h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg, 1 eV = 1.60 × 10-19)

Accepted Answer

A)  0.10 eV 
B)  0.052 eV 
C)  0.13 eV 
D)  0.078 eV 
E)  0.026 eV

Exam 38: Quantization

An electron is confined in a one-dimensional box (an infinite well) . Two adjacent allowed energies of the electron are 1.068 × 10^-18 J and 1.352 × 10^-18 J. What is the length of the box? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg)

An electron is in an infinite square well that is 2.6 nm wide. What is the smallest value of the state quantum number n for which the energy level exceeds 100 eV? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19)

Calculate the kinetic energy (in eV) of a nonrelativistic neutron that has a de Broglie wavelength of 9.9 × 10^-12 m. (h = 6.626 × 10^-34 J ∙ s, m_neutron = 1.675 × 10^-27 kg, 1 eV = 1.60 10^-19 J)

A laser emits light of wavelength 463 nm during a brief pulse that lasts for 25 ms and has a total energy of 1.2 J. How many photons are emitted in that single pulse? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s)

A hydrogen atom makes a downward transition from the n = 20 state to the n = 5 state. Find the wavelength of the emitted photon. The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s)

A metal surface has a work function of 1.50 eV. Calculate the maximum kinetic energy, in eV, of electrons ejected from this surface by electromagnetic radiation of wavelength 311 nm. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, e = - 1.60 × 10^-19 C, 1 eV = 1.60 × 10^-19 J)

How fast must a nonrelativistic electron move so its de Broglie wavelength is the same as the wavelength of a 3.4-eV photon? (m_el = 9.11 × 10^-31 kg, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

What is the orbital radius of the n = 3 excited state in the Bohr model of the hydrogen atom? The ground-state radius of the hydrogen atom is 0.529 × 10^-10 m.

A metal having a work function of 2.4 eV is illuminated with monochromatic light whose photon energy is 4.0 eV. What is the maximum kinetic energy of the photoelectrons produced by this light? (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

You want to have an electron in an energy level where its speed is no more than 66 m/s. What is the length of the smallest box (an infinite well) in which you can do this? (h = 6.626 × 10^-34 J ∙ s, M_el = 9.11 × 10^-31 kg)

When a certain metal is illuminated by light, photoelectrons are observed provided that the wavelength of the light is less than 669 nm. Which one of the following values is closest to the work function of this metal? (h = 6.626 × 10^-34J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

The Bohr radius of the hydrogen atom is 0.529 × 10^-10 m. What is the radius of the n = 2 state?

An electron is in an infinite square well (a box) that is 8.9 nm wide. What is the ground state energy of the electron? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19)

An 84-kW AM radio station broadcasts at 1000 kHz . How many photons are emitted each second by the transmitting antenna? (h = 6.626 × 10^-34 J ∙ s)

A gas of helium atoms (each of mass 6.65 × 10^-27 kg) are at room temperature of 20.0°C. What is the de Broglie wavelength of the helium atoms that are moving at the root-mean-square speed? (h = 6.626 × 10^-34 J ∙ s, the Boltzmann constant is 1.38 × 10^-23 J/K)

Exam 38: Quantization

An electron is confined in a one-dimensional box (an infinite well) . Two adjacent allowed energies of the electron are 1.068 × 10-18 J and 1.352 × 10-18 J. What is the length of the box? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg)

An electron is in an infinite square well that is 2.6 nm wide. What is the smallest value of the state quantum number n for which the energy level exceeds 100 eV? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg, 1 eV = 1.60 × 10-19)

Calculate the kinetic energy (in eV) of a nonrelativistic neutron that has a de Broglie wavelength of 9.9 × 10-12 m. (h = 6.626 × 10-34 J ∙ s, mneutron = 1.675 × 10-27 kg, 1 eV = 1.60 10-19 J)

A laser emits light of wavelength 463 nm during a brief pulse that lasts for 25 ms and has a total energy of 1.2 J. How many photons are emitted in that single pulse? (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s)

A hydrogen atom makes a downward transition from the n = 20 state to the n = 5 state. Find the wavelength of the emitted photon. The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J, c = 3.00 × 108 m/s)

A metal surface has a work function of 1.50 eV. Calculate the maximum kinetic energy, in eV, of electrons ejected from this surface by electromagnetic radiation of wavelength 311 nm. (c = 3.00 × 108 m/s, h = 6.626 × 10-34 J ∙ s, e = - 1.60 × 10-19 C, 1 eV = 1.60 × 10-19 J)

How fast must a nonrelativistic electron move so its de Broglie wavelength is the same as the wavelength of a 3.4-eV photon? (mel = 9.11 × 10-31 kg, c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J)

What is the orbital radius of the n = 3 excited state in the Bohr model of the hydrogen atom? The ground-state radius of the hydrogen atom is 0.529 × 10-10 m.

A metal having a work function of 2.4 eV is illuminated with monochromatic light whose photon energy is 4.0 eV. What is the maximum kinetic energy of the photoelectrons produced by this light? (h = 6.626 × 10-34 J ∙ s, 1 eV = 1.60 × 10-19 J)

You want to have an electron in an energy level where its speed is no more than 66 m/s. What is the length of the smallest box (an infinite well) in which you can do this? (h = 6.626 × 10-34 J ∙ s, Mel = 9.11 × 10-31 kg)

When a certain metal is illuminated by light, photoelectrons are observed provided that the wavelength of the light is less than 669 nm. Which one of the following values is closest to the work function of this metal? (h = 6.626 × 10-34 J ∙ s, c = 3.00 × 108 m/s, 1 eV = 1.60 × 10-19 J)

The Bohr radius of the hydrogen atom is 0.529 × 10-10 m. What is the radius of the n = 2 state?

An electron is in an infinite square well (a box) that is 8.9 nm wide. What is the ground state energy of the electron? (h = 6.626 × 10-34 J ∙ s, mel = 9.11 × 10-31 kg, 1 eV = 1.60 × 10-19)

An 84-kW AM radio station broadcasts at 1000 kHz . How many photons are emitted each second by the transmitting antenna? (h = 6.626 × 10-34 J ∙ s)

A gas of helium atoms (each of mass 6.65 × 10-27 kg) are at room temperature of 20.0°C. What is the de Broglie wavelength of the helium atoms that are moving at the root-mean-square speed? (h = 6.626 × 10-34 J ∙ s, the Boltzmann constant is 1.38 × 10-23 J/K)

An electron is confined in a one-dimensional box (an infinite well) . Two adjacent allowed energies of the electron are 1.068 × 10^-18 J and 1.352 × 10^-18 J. What is the length of the box? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg)

An electron is in an infinite square well that is 2.6 nm wide. What is the smallest value of the state quantum number n for which the energy level exceeds 100 eV? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19)

Calculate the kinetic energy (in eV) of a nonrelativistic neutron that has a de Broglie wavelength of 9.9 × 10^-12 m. (h = 6.626 × 10^-34 J ∙ s, m_neutron = 1.675 × 10^-27 kg, 1 eV = 1.60 10^-19 J)

A laser emits light of wavelength 463 nm during a brief pulse that lasts for 25 ms and has a total energy of 1.2 J. How many photons are emitted in that single pulse? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s)

A hydrogen atom makes a downward transition from the n = 20 state to the n = 5 state. Find the wavelength of the emitted photon. The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s)

A metal surface has a work function of 1.50 eV. Calculate the maximum kinetic energy, in eV, of electrons ejected from this surface by electromagnetic radiation of wavelength 311 nm. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, e = - 1.60 × 10^-19 C, 1 eV = 1.60 × 10^-19 J)

How fast must a nonrelativistic electron move so its de Broglie wavelength is the same as the wavelength of a 3.4-eV photon? (m_el = 9.11 × 10^-31 kg, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

What is the orbital radius of the n = 3 excited state in the Bohr model of the hydrogen atom? The ground-state radius of the hydrogen atom is 0.529 × 10^-10 m.

A metal having a work function of 2.4 eV is illuminated with monochromatic light whose photon energy is 4.0 eV. What is the maximum kinetic energy of the photoelectrons produced by this light? (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

You want to have an electron in an energy level where its speed is no more than 66 m/s. What is the length of the smallest box (an infinite well) in which you can do this? (h = 6.626 × 10^-34 J ∙ s, M_el = 9.11 × 10^-31 kg)

When a certain metal is illuminated by light, photoelectrons are observed provided that the wavelength of the light is less than 669 nm. Which one of the following values is closest to the work function of this metal? (h = 6.626 × 10^-34J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

The Bohr radius of the hydrogen atom is 0.529 × 10^-10 m. What is the radius of the n = 2 state?

An electron is in an infinite square well (a box) that is 8.9 nm wide. What is the ground state energy of the electron? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19)

An 84-kW AM radio station broadcasts at 1000 kHz . How many photons are emitted each second by the transmitting antenna? (h = 6.626 × 10^-34 J ∙ s)

A gas of helium atoms (each of mass 6.65 × 10^-27 kg) are at room temperature of 20.0°C. What is the de Broglie wavelength of the helium atoms that are moving at the root-mean-square speed? (h = 6.626 × 10^-34 J ∙ s, the Boltzmann constant is 1.38 × 10^-23 J/K)