Exam 27: Early Quantum Theory and Models of the Atom

A photocathode having a work function of $2.4 \mathrm { eV }$ is illuminated with monochromatic light whose photon energy is $3.4 \mathrm { eV }$ . What is maximum kinetic energy of the photoelectrons produced? $( c = 3.00$ $\times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )

What is the wavelength of the photon emitted when an electron in a hydrogen atom which is in the initial state $n = 8$ jumps to the final state $n = 2 ? \left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = \right.$ $1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )

A certain crystal has a spacing of $0.442 \mathrm {~nm}$ between atoms. A beam of neutrons moving with a speed of $1640 \mathrm {~m} / \mathrm { s }$ perpendicular to the surface is diffracted as it passes through the crystal. What is the angle from the central maximum to the next interference maximum? ( $m$ neutron $= 1.675 \times$ $\left. 10 ^ { - 27 } \mathrm {~kg} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

What is the longest wavelength in the Balmer series?

What is the shortest wavelength of the Lyman series?

What is the energy (in eV) of an optical photon of frequency $6.43 \times 10 ^ { 14 } \mathrm {~Hz} . \left( h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right.$ , $1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )

After an electron has been accelerated through a potential difference of $0.15 \mathrm { kV }$ , what is its de Broglie wavelength? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

For what wavelength does a $100 - \mathrm { mW }$ laser beam deliver $1.6 \times 1017$ photons in one second? $( c = 3.0$ $\left. \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

Light with a wavelength of $310 \mathrm {~nm}$ is incident on a metal that has a work function of $3.80 \mathrm { eV }$ . What is the maximum kinetic energy that a photoelectron ejected in this process can have? $( 1 \mathrm { eV } = 1.60 \times$ $\left. 10 - 19 \mathrm {~J} , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

An electron is accelerated from rest through a potential difference. After acceleration the electron has a wavelength of $880 \mathrm {~nm}$ . What is the potential difference responsible for the acceleration of the electron? \left( h = 6.626 \times 10 <sup>- 34</sup> \mathrm {~J} \cdot \mathrm { s } , m _ { \text {electron } } = 9.11 \times 10<sup> - 31</sup> \mathrm {~kg} , e = 1.6*10<sup>- 19</sup> \mathrm { C } \right) A) $2.5 \times 10 ^ { - 6 } \mathrm {~V}$ B) $1.7 \times 10 ^ { - 6 } \mathrm {~V}$ C) $2.2 \times 10 ^ { - 6 } \mathrm {~V}$ D) $1.9 \times 10 ^ { - 6 } \mathrm {~V}$

What is the wavelength of the emitted photon if an electron in the hydrogen atom makes a transition from the $n = 7$ state to the $n = 2$ state? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = \right.$ $1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )

Monochromatic light falls on a metal surface and electrons are ejected. If the intensity of the light is increased, what will happen to the ejection rate and maximum energy of the electrons?

A certain photon, after being scattered from a free electron that was at rest, moves at an angle of $120 ^ { \circ }$ with respect to the incident direction. If the wavelength of the incident photon is $0.6110 \mathrm {~nm}$ , what is the kinetic energy of the recoiling electron? $\left( m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right.$ , $\left. h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

If the frequency of a light beam is doubled, what happens to the momentum of the photons in that beam of light?

If the momentum of an electron is $1.95 \times 10 ^ { - 27 } \mathrm {~kg} \cdot \mathrm { m } / \mathrm { s }$ , what is its de Broglie wavelength? $( h =$ $6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s }$ )

A certain photon, after being scattered from a free electron that was at rest, moves at an angle of $120 ^ { \circ }$ with respect to the incident direction. If the wavelength of the incident photon is $0.591 \mathrm {~nm}$ , what is the wavelength of the scattered photon? (melectron $= 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$ , $h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s }$ )

A metal surface has a work function of $2.50 \mathrm { eV }$ . What is the longest wavelength of light that will eject electrons from the surface of this metal? $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , c = 3.00 \times 10 ^ { 8 } \right.$ $\mathrm { m } / \mathrm { s } , h = 6.626 \times 10^{- 34} \mathrm {~J} \cdot \mathrm { s } )$

The Bohr model of the hydrogen atom predicts an ionization energy of $13.6 \mathrm { eV }$ . Using this model, what would we expect for the ionization energy of the $\mathrm { Li } ^ { + + }$ ion, which has 3 protons?

Electrons emerge from an electron gun with a speed of $2.0 \times 10 ^ { 6 } \mathrm {~m} / \mathrm { s }$ and then pass through a double-slit apparatus. Interference fringes with spacing of $2.7 \mathrm {~mm}$ are detected on a screen far from the double slit. What would the fringe spacing be if the electrons were replaced by neutrons with the same speed? $\left( h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , m _ { \text {neutron } } = 1.675 \times \right.$ 10-27 $\mathrm { kg }$ )

Each photon in a beam of light has an energy of $4.20 \mathrm { eV }$ . What is the wavelength of this light? $( c =$ $3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )