Exam 27: Early Quantum Theory and Models of the Atom

For a certain metal, light of frequency $7.24 \times 10 ^ { - 14 } \mathrm {~Hz}$ is just barely able to dislodge photoelectrons from the metal. $\left( h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , e = 1.60 \times \right.$ $10 ^ { - 19 } \mathrm { C }$ ) (a) What will be the stopping potential if light of frequency $8.75 \times 10 ^ { - 14 } \mathrm {~Hz}$ is shone on the metal? (b) What is the work function (in electron-volts) of this metal?

Consider the Bohr model for the hydrogen atom in its second excited state. (a) Determine the binding energy $( \mathrm { eV } )$ of the electron. (b) What is the radius of the electron orbit, given that $r _ { 1 } = 0.0529 \mathrm {~nm}$ ? (c) How far is it from the next higher excited orbit?

The work function of a certain metal is $1.90 \mathrm { eV }$ . What is the longest wavelength of light that can cause photoelectron emission from this metal? $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times \right.$ 10>^-34 J.s)

The distance between adjacent orbits in a hydrogen atom

Monochromatic light is incident on a metal surface, and the ejected electrons give rise to a current in the circuit shown in the figure. The maximum kinetic energy of the ejected electrons is determined by applying a reverse ('stopping') potential, sufficient to reduce the current in the ammeter to zero. If the intensity of the incident light is increased, how will the required stopping potential change?

A proton and an electron are both accelerated to the same final kinetic energy. If $\lambda _ { p }$ is the de Broglie wavelength of the proton and $\lambda _ { \mathrm { e } }$ is the de Broglie wavelength of the electron, then

What is the shortest wavelength of a photon that can be emitted by a hydrogen atom, for which the initial state is $n = 3 ? \left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} \right)$

What is the momentum of a photon of light that has a wavelength of $480 \mathrm {~nm}$ ? $\left( h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

When it is struck by $240 - \mathrm { nm }$ photons, a material having a work function of $2.60 \mathrm { eV }$ emits electrons. What is the maximum kinetic energy of the emitted electrons? ( $c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times$ $10 ^{- 34} \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^{- 19} \mathrm {~J}$ )

Hydrogen atoms can emit four spectral lines with visible colors from red to violet. These four visible lines emitted by hydrogen atoms are produced by electrons

What is the wavelength of a $6.32 - \mathrm { eV }$ photon? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \right.$ $\times 10 ^ { - 19 } \mathrm {~J}$ )

If the de Broglie wavelength of an electron is $380 \mathrm {~nm}$ , what is the speed of this electron? (melectron $\left. = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

The electrons in a beam are moving at $18 \mathrm {~m} / \mathrm { s }$ . ( $m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , h = 6.626 \times$ $10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s }$ ) (a) What is its de Broglie wavelength these electrons? (b) If the electron beam falls normally on a diffraction grating, what would have to be the spacing between slits in the grating to give a first-order maximum at an angle of $30 ^ { \circ }$ with the normal to the grating?

A photocathode having a work function of $2.8 \mathrm { eV }$ is illuminated with monochromatic electromagnetic radiation whose photon energy is $4.0 \mathrm { eV }$ . What is the threshold (cutoff) frequency for photoelectron production? $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

A hydrogen atom with a barely bound electron may have an average radius as large as a bacterium, which is a radius of $14 \mu \mathrm { m }$ . What is the nearest principal quantum number of the atom in this state? The radius for ground state hydrogen is $0.0529 \mathrm {~nm}$ .

What is the longest wavelength in the Lyman Series?

A crystal diffracts a beam of electrons, like a diffraction grating, as they hit it perpendicular to its surface. The crystal spacing is $0.18 \mathrm {~nm}$ , and the first maximum scattering occurs at $80 ^ { \circ }$ relative to the normal to the surface. $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , m _ { \mathrm { e } } \right.$ ectron $\left. = 9.11 \times 10 ^ { - 13 } \mathrm {~kg} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$ (a) What is the wavelength of the electrons? (b) What potential difference accelerated the electrons if they started from rest?

The wavelength of the emitted photon if an electron in the hydrogen atom makes a transition from the $n = 2$ state to the ground state is closest to which of the following values? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = \right.$ $6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )

Increasing the brightness of a beam of light without changing its color will increase

A highly ionized atom with $Z = 5$ has only one electron left around it, in its ground state. How much more energy is required to finish the job and have a bare nucleus?