Exam 38: Quantization

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 × m/s? (m_proton = 1.67 × 10^-27 kg,c = 3.00 × 10⁸ m/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)

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.

Light shines through atomic hydrogen gas.It is seen that the gas absorbs light readily at a wavelength of 91.63 nm.What is the value of n of the level to which the hydrogen is being excited by the absorption of light of this wavelength? Assume that the most of the atoms in the gas are in the lowest level.(h = 6.626 × 10^-34 J ∙ s,c = 3.00 × 10⁸ m/s,1 eV = 1.60 × 10^-19 J,the Rydberg constant is R = 1.097 × 10⁷ m^-1.)

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)

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?

In a double slit experiment,a beam of electrons strikes a pair of slits.The slits are 15 μm apart,and the first interference maximum lies at an angle of 0.50 µrad from the center of the interference pattern.What is the momentum of the incoming electrons? (h = 6.626 × 10^-34 J ∙ s,m_el = 9.11 × 10^-31 kg)

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 hydrogen atom is excited to the n = 10 stated.It then decays to the n = 4 state by emitting a photon which is detected in a photographic plate.What is the frequency 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)

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?

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

A beam of x-rays at a certain wavelength are scattered from a free electron at rest and the scattered beam is observed at 45.0° to the incident beam.What is the change in the wavelength of the X-rays? (m_el = 9.11 × 10^-31 kg,h = 6.626 × 10^-34 J ∙ s,c = 3.00 × 10⁸ m/s)

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 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)

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?

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)

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)

Electrons emerge from an electron gun with a speed of 2.0 × 10⁶ m/s and then pass through a pair of thin parallel slits.Interference fringes with a spacing of 2.7 mm are detected on a screen far from the double slit and fairly close to the center of the pattern.What would the fringe spacing be if the electrons were replaced by neutrons with the same speed? (m_el = 9.11 × 10^-31 kg,m_neutron = 1.67 × 10^-27 kg)

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 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)