Exam 27: Early Quantum Theory and Models of the Atom

Two sources emit beams of light of wavelength $550 \mathrm {~nm}$ . The light from source A has an intensity of $10 \mu \mathrm { W } / \mathrm { m } ^ { 2 }$ , and the light from source $B$ has an intensity of $20 \mu \mathrm { W } / \mathrm { m } ^ { 2 }$ . This is all we know about the two beams. Which of the following statements about these beams are correct? (There could be more than one correct choice.)

The Paschen series is formed by electron transitions that

If a proton and an electron have the same speed, which one has the longer de Broglie wavelength?

If the de Broglie wavelength of an electron is $2.4 \mu \mathrm { m }$ , what is the speed of the electron? (melectron $= 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s }$ )

Which of the following actions will increase the energy of a photon? (There could be more than one correct choice.)

An $18.0$ pm wavelength photon is scattered by a stationary electron through an angle of $120 ^ { \circ }$ . What is the wavelength of the scattered photon? (melectron $= 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h$ $\left. = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

The spacing of the atoms of a crystal is $159 \mathrm { pm }$ . A monoenergetic beam of neutrons directed normally at the surface of the crystal undergoes first order diffraction at an angle of $58 ^ { \circ }$ from the normal. What is the energy of each of the neutrons? ( $m _ { \text {neutron } } = 1.675 \times 10 ^ { - 27 } \mathrm {~kg} , 1 \mathrm { eV } = 1.6 \times$ $\left. 10 ^ { - 19 } \mathrm {~J} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

What is the wavelength of the photon emitted when an electron in a hydrogen atom which is in the initial state $n = 4$ jumps to the final state $n = 2$ ? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = \right.$ $1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )

An ionized atom having Z protons has had all but one of its electrons removed. If R is the radius of the ground state electron orbit in atomic hydrogen, then what is the radius of the shell of the Remaining electron in the ionized atom?

If the work function of a metal surface is $2.20 \mathrm { eV }$ , what frequency of incident light would give a maximum kinetic energy of $0.25 \mathrm { eV }$ to the photoelectrons ejected from this surface? $( 1 \mathrm { eV } = 1.60 \times$ $\left. 10 ^{- 19} \mathrm {~J} , h = 6.626 \times 10 ^{- 34}\mathrm {~J} \cdot \mathrm { s } \right)$

When an electron jumps from an orbit where n = 4 to one where n = 2

When a photoelectric surface is illuminated with light of wavelength $437 \mathrm {~nm}$ , the stopping potential is measured to be $1.67 \mathrm {~V} . \left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , e = 1.60 \times 10 ^ { - 19 } \mathrm { C } , m _ { \mathrm { e } } \right.$ ectron = $\left. 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$ (a) What is the work function of the metal, in $\mathrm { eV }$ ? (b) What is the maximum speed of the ejected electrons?

A small gas laser of the type used in classrooms may radiate light at a power level of $2.0$ $\mathrm { mW }$ . If the wavelength of the laser light is $642 \mathrm {~nm}$ , how many photons does it emit per second? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

The shortest wavelength of a photon that can be emitted by a hydrogen atom, for which the initial state is $n = 12$ , is closest to which one of the following values? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right.$ , $h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )

What is the ground state energy of the $\mathrm { Li } ^ { + + }$ ion, which has atomic number 3 ?

An electron has the same de Broglie wavelength as the wavelength of a $1.8 \mathrm { eV }$ photon. What is the speed of the electron? ( $m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )

Photon A has twice the momentum of photon B as both of them are traveling in vacuum. Which statements about these photons are correct? (There could be more than one correct choice.)

What is the wavelength of a photon having energy $2.00 \mathrm { eV } ? \left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times \right.$ $10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )

The Lyman series is formed by electron transitions in hydrogen that

The Iongest wavelength photon that can be emitted by a hydrogen atom, for which the final state is $n = 9$ , is closest to which one of the following values? $\left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} \right.$ , $\left. h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$