Exam 38: Quantization

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 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)

In a particular case of Compton scattering, a photon collides with a free electron and scatters backwards. The wavelength after the collision is exactly double the wavelength before the collision. What is the wavelength of the incident photon? (m_el = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s)

X-rays of energy 2.9 × 10⁴ eV are scattered by a free stationary electron through an angle of 135°. What is the energy of the scattered X-rays, in electron volts? (m_el = 9.11 × 10^-31 kg, e = - 1.60 × 10^-19 C, h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A hydrogen atom initially in the n = 6 state decays to the n = 2 state. The emitted photon is detected in a photographic plate. What is the wavelength of the detected 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 beam of red light and a beam of violet light each deliver the same power on a surface. For which beam is the number of photons hitting the surface per second the greatest?

What is the orbital radius of the 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 photon of initial wavelength 0.651 nm, after being scattered from a free electron at rest, moves off at an angle of 120° with respect to its incident direction. (m_el = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s) (a) What is the wavelength of the scattered photon? (b) What is the energy of the scattered photon?

A hydrogen atom makes a downward transition from the 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)

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 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, m_el = 9.11 × 10^-31 kg)

Light of wavelength 400 nm falls on a metal surface having a work function 1.70 eV. What is the maximum kinetic energy of the photoelectrons emitted from the metal? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s = 4.141 × 10^-15 ev ∙ 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)

A hydrogen atom is in its n = 2 excited state when its electron absorbs a photon of energy . What is the energy of the resulting free electron? 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)

A photon of wavelength 29 pm is scattered by a stationary electron. What is the maximum possible energy loss of the photon? (m_el = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s)

A single slit is illuminated at normal incidence with a parallel beam of light having a wavelength of 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)

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 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)

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)

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?