Exam 27: Early Quantum Theory and Models of the Atom

When the surface of a metal is exposed to blue light, electrons are emitted. If the intensity of the blue light is increased, which of the following things will also increase?

If the scattering angle of the light in Compton's scattering experiment is $90 ^ { \circ }$ , what is the change in the wavelength of the light? ( $m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s }$ )

Electrons are accelerated to a speed of $4.0 \times 10 ^ { 4 } \mathrm {~m} / \mathrm { s }$ and are then aimed at a double-slit apparatus, where interference fringes are detected. If the electrons were replaced by neutrons, what speed must neutrons have to produce interference fringes with the same fringe spacing as that observed with the electrons? $\left( h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , m _ { \text {neutron } } = 1.675 \times 10 ^ { - 27 } \right.$ $\mathrm { kg }$ )

If you double the frequency of the light in a laser beam, but keep the number of photons per second in the beam fixed, which of the following statements are correct? (There could be more Than one correct choice.)

A photocathode whose work function is $2.9 \mathrm { eV }$ is illuminated with white light that has a continuous wavelength band from $400 \mathrm {~nm}$ to $700 \mathrm {~nm}$ . What is the range of the wavelength band in this white light illumination for which photoelectrons are not produced? $( c = 3.00 \times 10^8 \mathrm {~m} / \mathrm { s } , h = 6.626$ $\times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )

Protons are being accelerated in a particle accelerator. When the energy of the protons is doubled, their de Broglie wavelength will

What is the wavelength of the most intense light emitted by a giant star of surface temperature 5000 K? The constant in Wien's law is 0.00290 m · K.

A blue laser beam is incident on a metallic surface, causing electrons to be ejected from the metal. If the frequency of the laser beam is increased while the intensity of the beam is held fixed,

A beam of X-rays at a certain wavelength are scattered from a free electron that is at rest, and the scattered beam is observed at $45.0 ^ { \circ }$ from the incident beam. What is the change in the wavelength of the $\mathrm { x }$ -rays during this process? (melectron $= 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times$ 10^-34J.s)

What value of n corresponds to a wavelength of 91.7 nm in the Lyman series?

What is the energy of the photon emitted when an electron drops from the $n = 20$ state to the $n = 7$ state in a hydrogen atom?

In her physics laboratory, Mathilda shines electromagnetic radiation on a material and collects photoelectric data to determine Planck's constant. She measures a stopping potential of $5.82 \mathrm {~V}$ for radiation of wavelength $100 \mathrm {~nm}$ , and $17.99 \mathrm {~V}$ for radiation of wavelength $50.0 \mathrm {~nm} . \left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$ (a) Using Mathilda's data, what value does she determine for Planck's constant? (b) What is the work function of the material Mathilda is using, in electron-volts?

How much energy is carried by a photon of light having frequency $110 \mathrm { GHz }$ ? $\left( h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \right.$ . s)

To which of the following values of $n$ does the longest wavelength in the Balmer series correspond?

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 energy of the scattered photon? (melectron $= 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s }$ , $h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s }$ )

What is the shortest wavelength in the Balmer series?

$\mathrm { X }$ -rays with a wavelength of $0.00100 \mathrm {~nm}$ are scattered at $130 ^ { \circ }$ by free electrons. What is the kinetic energy of each recoil electron? $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} \right.$ , melectron $= 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , c = 3.00 \times 10 ^ { 8 }$ $\left. \mathrm { m } / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

What is the ionization energy of singly-ionized helium, which has 2 protons?

An x-ray tube accelerates electrons through a potential difference of $50.0 \mathrm { kV }$ . If an electron in the beam suddenly give up its energy in a collision, what is the shortest wavelength x-ray it could produce? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

What is the longest wavelength of electromagnetic radiation that will eject photoelectrons from sodium metal for which the work function is $2.28 \mathrm { eV }$ ? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \right.$ $\mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )