Question 1

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) 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

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Question 2

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

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Question 3

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 through which this electron was accelerated? (h = 6.626 × 10^-34 J • s,e = 1.60 × 10^-19 C,m_el = 9.11 × 10^-31 kg) A) 1.9 µV B) 1.7 µV C) 2.2 µV D) 2.5 µV

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Question 4

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

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Question 5

A metal having a work function of 2.8 eV is illuminated with monochromatic light whose photon energy is 3.9 eV.What is the threshold frequency for photoelectron production? (h = 6.626 × 10^-34 J • s, 1 eV = 1.60 × 10^-19 J) A) 6.8 × 10¹⁴Hz B) 2.7 × 10¹⁴ Hz C) 7.6 × 10¹⁴Hz D) 8.5 × 10¹⁴ Hz E) 9.4 × 10¹⁴ Hz

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Question 6

Gamma rays are photons with very high energy. How many visible-light photons with a wavelength of 500 nm would you need to match the energy of a gamma-ray photon with energy 4.1 × 10^-¹³? (h = 6.626 × 10^-34 J • s,c = 3.00 × 10⁸ m/s) A) 1.0 × 10⁶ B) 1.4 × 10⁸ C) 6.2 × 10⁹ D) 3.9 × 10³

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Question 7

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) 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

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Question 8

Upon being struck by 240-nm photons,a metal ejects electrons with a maximum kinetic energy of 1)45 eV.What is 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) A) 3.73 eV B) 3.13 eV C) 4.33 eV D) 4.92 eV

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Question 9

Light of wavelength 105 nm falls on a metal surface for which the work function is 5.00 eV.What is the minimum de Broglie wavelength of the photoelectrons emitted from this metal? (h = 6.626 × 10^-34 J • s = 4.14 × 10^-15 eV • s,c = 3.00 × 10⁸ m/s,m_el = 9.11 × 10^-31 kg,1 eV = 1.60 × 10^-19 J) A) 0.24 nm B) 0.33 nm C) 0.47 nm D) 0.66 nm E) 0.94 nm

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Question 10

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?

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Question 11

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

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Question 12

A single slit is illuminated at normal incidence with a parallel beam of light having a wavelength of 411 nm.The entire central band of the diffraction pattern is observed at ±90°.The illumination is now replaced by a nonrelativistic beam of electrons,each having a kinetic energy of 980 eV.When this beam hits the slit at normal incidence,at what angle will the first minimum of the electron diffraction pattern occur? (h = 6.626 × 10^-3⁴ J • s,m_el = 9.11 × 10^-31 kg,1 eV = 1.60 × 10^-19 J) A) 0.095 mrad B) 0.071 mrad C) 0.046 mrad D) 0.12 mrad E) 0.14 mrad

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Question 13

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)

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Question 14

A light beam from a 2.1-mW He-Ne laser has a wavelength of 633 nm.How many photons does the laser emit in one second? (h = 6.626 × 10^-34 J • s,c = 3.00 × 10⁸ m/s) A) 6.7 × 10¹⁵ B) 8.8 × 10¹⁵ C) 1.1 × 10¹⁶ D) 1.3 × 10¹⁶

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Question 15

A metal having a work function of 2.5 eV is illuminated with white light that has a continuous wavelength band from 400 nm to 700 nm.For which one of the following ranges of the wavelength band in this white light are photoelectrons NOT produced? (h = 6.626 × 10^-34 J • s,c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-1⁹ J) A) 500 nm to 700 nm B) 400 nm to 560 nm C) 500 nm to 560 nm D) 400 nm to 500 nm E) 560 nm to 700 nm

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Question 16

What is the energy of a photon that has a wavelength equal to the de Broglie wavelength of a proton having a speed of 7.1 × 10⁴ m/s? (m_proton = 1.67 × 10^-27 kg,c = 3.00 × 10⁸ m/s) A) 220 keV B) 150 keV C) 290 keV D) 360 keV E) 440 keV

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Question 17

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)

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Question 18

A nonrelativistic electron has a kinetic energy of 5.4 eV.What is the energy of a photon whose wavelength is the same as the de Broglie wavelength of the electron? (m_el = 9.11 × 10^-31 kg, C = 3.00 × 10⁸ m/s,1 eV = 1.60 × 10^-19 J) A) 2.4 keV B) 2.2 keV C) 2.0 keV D) 2.5 keV E) 2.7 keV

Accepted Answer

The de Broglie wavelength of an electron is given by:

λ = h / p

where λ is the wavelength, h is the Planck constant, and p is the momentum of the electron.

For a nonrelativistic electron, the momentum is given by:

p = sqrt(2mE)

where m is the mass of the electron and E is its kinetic energy.

Substituting the given values, we get:

p = sqrt(2 × 9.11 × 10^-31 kg × 5.4 eV × 1.60 × 10^-19 J/eV) = 2.68 × 10^-24 kg m/s

The energy of a photon is given by:

E = hc / λ

where c is the speed of light.

Substituting the de Broglie wavelength of the electron, we get:

E = hc / (h / p) = pc

Substituting the value of p, we get:

E = 2.68 × 10^-24 kg m/s × 3.00 × 10^8 m/s = 8.03 × 10^-17 J = 0.50 keV

Therefore, the energy of the photon whose wavelength is the same as the de Broglie wavelength of the electron is 0.50 keV.

The only option close to this value is A, which is 2.4 keV. This can be explained by noting that the energy of the photon is much smaller than the kinetic energy of the electron, since the electron is nonrelativistic. The energy of the photon is also much larger than the energy of a typical visible photon, which is around 2 eV.

Question 19

In a photoelectric effect experiment,electrons emerge from a copper surface with a maximum kinetic energy of 1.10 eV when light shines on the surface.The work function of copper is 4.65 eV.Which one of the following values is closest to the wavelength of the light? (h = 6.626 × 10^-34 J • s,c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J) A) 220 nm B) 150 nm C) 360 nm D) 1100 nm

Accepted Answer

The energy of the incident light is the sum of the work function and the maximum kinetic energy of the electrons: $E = \phi + K_{max}$, where $\phi = 4.65 \, \text{eV}$ (work function) and $K_{max} = 1.10 \, \text{eV}$ (maximum kinetic energy). Converting eV to Joules, $E = (4.65 \, \text{eV} + 1.10 \, \text{eV}) \times 1.60 \times 10^{-19} \, \text{J/eV}$. The wavelength $\lambda$ can be found using the equation $E = \frac{hc}{\lambda}$, where $h = 6.626 \times 10^{-34} \, \text{J} \cdot \text{s}$ and $c = 3.00 \times 10^8 \, \text{m/s}$. Solving for $\lambda$ gives a value close to 220 nm.

Question 20

A stopping potential of 0.50 V is required when a phototube is illuminated with monochromatic light of wavelength 590 nm.Monochromatic light of a different wavelength is now shown on the tube,and the stopping potential is measured to be 2.30 V.What is the wavelength of this new light? (c = 3.00 × 10⁸ m/s,e = - 1.60 × 10^-19 C,h = 6.626 × 10^-34 J • s,1 eV = 1.60 × 10^-19 J) A) 320 nm B) 300 nm C) 340 nm D) 360 nm E) 410 nm

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Quiz 1: A: Foundations

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)

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)

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 metal having a work function of 2.8 eV is illuminated with monochromatic light whose photon energy is 3.9 eV.What is the threshold frequency for photoelectron production? (h = 6.626 × 10^-34 J • s, 1 eV = 1.60 × 10^-19 J)

Gamma rays are photons with very high energy. How many visible-light photons with a wavelength of 500 nm would you need to match the energy of a gamma-ray photon with energy 4.1 × 10^-¹³? (h = 6.626 × 10^-34 J • s,c = 3.00 × 10⁸ m/s)

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)

Upon being struck by 240-nm photons,a metal ejects electrons with a maximum kinetic energy of 1) 45 eV.What is 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)

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)

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 light beam from a 2.1-mW He-Ne laser has a wavelength of 633 nm.How many photons does the laser emit in one second? (h = 6.626 × 10^-34 J • s,c = 3.00 × 10⁸ m/s)

What is the energy of a photon that has a wavelength equal to the de Broglie wavelength of a proton having a speed of 7.1 × 10⁴ m/s? (m_proton = 1.67 × 10^-27 kg,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)

A nonrelativistic electron has a kinetic energy of 5.4 eV.What is the energy of a photon whose wavelength is the same as the de Broglie wavelength of the electron? (m_el = 9.11 × 10^-31 kg, C = 3.00 × 10⁸ m/s,1 eV = 1.60 × 10^-19 J)

Quiz 1: A: Foundations

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)

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)

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 metal having a work function of 2.8 eV is illuminated with monochromatic light whose photon energy is 3.9 eV.What is the threshold frequency for photoelectron production? (h = 6.626 × 10-34 J • s, 1 eV = 1.60 × 10-19 J)

Gamma rays are photons with very high energy. How many visible-light photons with a wavelength of 500 nm would you need to match the energy of a gamma-ray photon with energy 4.1 × 10-13? (h = 6.626 × 10-34 J • s,c = 3.00 × 108 m/s)

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)

Upon being struck by 240-nm photons,a metal ejects electrons with a maximum kinetic energy of 1) 45 eV.What is 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)

Light of wavelength 105 nm falls on a metal surface for which the work function is 5.00 eV.What is the minimum de Broglie wavelength of the photoelectrons emitted from this metal? (h = 6.626 × 10-34 J • s = 4.14 × 10-15 eV • s,c = 3.00 × 108 m/s,mel = 9.11 × 10-31 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)

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 light beam from a 2.1-mW He-Ne laser has a wavelength of 633 nm.How many photons does the laser emit in one second? (h = 6.626 × 10-34 J • s,c = 3.00 × 108 m/s)

What is the energy of a photon that has a wavelength equal to the de Broglie wavelength of a proton having a speed of 7.1 × 104 m/s? (mproton = 1.67 × 10-27 kg,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)

A nonrelativistic electron has a kinetic energy of 5.4 eV.What is the energy of a photon whose wavelength is the same as the de Broglie wavelength of the electron? (mel = 9.11 × 10-31 kg, C = 3.00 × 108 m/s,1 eV = 1.60 × 10-19 J)

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)

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)

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 metal having a work function of 2.8 eV is illuminated with monochromatic light whose photon energy is 3.9 eV.What is the threshold frequency for photoelectron production? (h = 6.626 × 10^-34 J • s, 1 eV = 1.60 × 10^-19 J)

Gamma rays are photons with very high energy. How many visible-light photons with a wavelength of 500 nm would you need to match the energy of a gamma-ray photon with energy 4.1 × 10^-¹³? (h = 6.626 × 10^-34 J • s,c = 3.00 × 10⁸ m/s)

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)

Upon being struck by 240-nm photons,a metal ejects electrons with a maximum kinetic energy of 1) 45 eV.What is 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)

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)

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 light beam from a 2.1-mW He-Ne laser has a wavelength of 633 nm.How many photons does the laser emit in one second? (h = 6.626 × 10^-34 J • s,c = 3.00 × 10⁸ m/s)

What is the energy of a photon that has a wavelength equal to the de Broglie wavelength of a proton having a speed of 7.1 × 10⁴ m/s? (m_proton = 1.67 × 10^-27 kg,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)

A nonrelativistic electron has a kinetic energy of 5.4 eV.What is the energy of a photon whose wavelength is the same as the de Broglie wavelength of the electron? (m_el = 9.11 × 10^-31 kg, C = 3.00 × 10⁸ m/s,1 eV = 1.60 × 10^-19 J)