Exam 27: Early Quantum Theory and Models of the Atom

The cosmic background radiation permeating the universe has the spectrum of a $2.7 - \mathrm { K }$ blackbody radiator. What is the peak wavelength of this radiation? The constant in Wien's law is $0.0029 \mathrm {~m} \cdot \mathrm { K }$ .

What is the energy required to remove the electron from a hydrogen atom in the $n = 11$ state?

Light shines through atomic hydrogen gas that was initially in its ground state. You observe that after awhile much of the hydrogen gas has been excited to its $n = 5$ state. What wavelength of light entering the gas caused this excitation? \left( c = 3.00 \times 10<sup> 8 </sup>} \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10<sup> - 34</sup> \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times \right. 10^-19 J) A) $2280 \mathrm {~nm}$ B) $91.4 \mathrm {~nm}$ C) $95.2 \mathrm {~nm}$ D) $110 \mathrm {~nm}$

$\mathrm { X }$ -rays of wavelength $0.20 \mathrm {~nm}$ are scattered by a free electron. The change in the wavelength of the x-rays is observed to be $2.0 \times 10 ^ { - 12 } \mathrm {~m}$ at a certain scattering angle measured relative to the incoming x-ray direction. What is the scattering angle of the $x$ -rays? $\left( m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} \right.$ , $\left. c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

A metallic surface is illuminated with light of wavelength $400 \mathrm {~nm}$ . If the work function for this metal is $2.40 \mathrm { eV }$ , what is the maximum kinetic energy of the ejected electrons, in electron-volts? $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

What is the frequency of the most intense radiation from an object with temperature $100 ^ { \circ } \mathrm { C }$ ? The constant in Wien's law is $0.0029 \mathrm {~m} \cdot \mathrm { K } . \left( c = 3.0 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$

Light of a given wavelength is used to illuminate the surface of a metal, however, no photoelectrons are emitted. In order to cause electrons to be ejected from the surface of this metal You should

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

X-rays of energy $3.5 \times 10 ^ { 4 } \mathrm { eV }$ scatter through an angle of $105 ^ { \circ }$ off of a free electron. What is the energy (in eV) of the scattered x-rays? (melectron $= 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , c = 3.00 \times 10 ^ { 8 }$ $\mathrm { m } / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )

If a hydrogen atom in the ground state absorbs a photon of energy $12.09 \mathrm { eV }$ , to which state will the electron make a transition?

What is the wavelength of the matter wave associated with an electron moving with a speed of $2.5$ $\times 10 ^ { 7 } \mathrm {~m} / \mathrm { s }$ ? (melectron $\left. = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

Radio astronomers often study the radiation emitted by a hydrogen atom from a transition between the two hyperfine levels associated with the ground state. This radiation has a wavelength of $21 \mathrm {~cm}$ . What is the energy difference between the hyperfine levels? $( 1 \mathrm { eV } = 1.60 \times$ 10^-19J) A) $5.9 \times 10 ^ { - 6 } \mathrm { eV }$ B) $4.7 \times 10 ^ { - 25 } \mathrm {~J}$ C) $5.9 \times 10 ^ { - 25 } \mathrm {~J}$ D) $1.7 \times 10 ^ { - 24 } \mathrm {~J}$

Which of the following statements are true for the Bohr model of the atom? (There could be more than one correct choice.)

The Balmer series is formed by electron transitions in hydrogen that

The wavelength of a ruby laser is $694.3 \mathrm {~nm}$ . What is the energy difference between the two energy states for the transition that produces this light? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , h = 6.626 \right.$ $\times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s }$ )

What is the longest wavelength of light that can cause photoelectron emission from a metal that has a work function of $2.20 \mathrm { eV } ? \left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

Given that the binding energy of the hydrogen atom in its ground state is $- 13.6 \mathrm { eV }$ , what is the energy when it is in the $n = 5$ state?

If the Iongest wavelength of light that is able to dislodge electrons from a metal is $373 \mathrm {~nm}$ , what is the work function of that metal, in electron-volts? $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , c = 3.00 \times \right.$ $\left. 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

Light with a frequency of $8.70 \times 1014 \mathrm {~Hz}$ is incident on a metal that has a work function of $2.80 \mathrm { eV }$ . What is the maximum kinetic energy that a photoelectron ejected in this process can have? $( 1 \mathrm { eV } =$ $\left. 1.60 \times 10 ^ { - 19 } \mathrm {~J} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

If the wavelength of a photon in vacuum is the same as the de Broglie wavelength of an electron, which one is traveling faster through space?