Exam 27: Early Quantum Theory and Models of the Atom

A monochromatic light beam is incident on the surface of a metal having a work function of $2.50$ $\mathrm { eV }$ . If a $1.0 - \mathrm { V }$ stopping potential is required to make the electron current zero, what is the wavelength of light? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} \right)$

What is the value of n in the Balmer series for which the wavelength is 410.2 nm.

The figure shows part of the energy level diagram of a certain atom. The energy spacing between levels 1 and 2 is twice that between 2 and 3 . If an electron makes a transition from level 3 to level 2 , the radiation of wavelength $\lambda$ is emitted. What possible radiation wavelengths might be produced by other transitions between the three energy levels?

What is the wavelength of a photon having the same momentum as an electron that is traveling at $7.5 \mathrm {~km} / \mathrm { s }$ ? $\left( h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} \right)$

In a transition from one vibrational state to another, a molecule emits a photon of wavelength $5.56$ $\mu \mathrm { m }$ . What is the energy difference between these two states? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \right.$ $\cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )

A hydrogen atom is excited to the $n = 11$ level. Its decay to the $n = 7$ level is detected in a photographic plate. What is the wavelength of the light photographed? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , 1 \mathrm { eV } = \right.$ $\left. 1.60 \times 10 ^ { - 19 } \mathrm {~J} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

What frequency must a photon have to raise an electron in a hydrogen atom from the $n = 2$ to the $n$ $= 4$ state? $\left( h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} \right)$

What are the wavelength and the corresponding photon energy (in electron-volts) of the primary light emitted by an ideal blackbody at each of the following temperatures? $( c =$ $3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ , and the constant in Wein's law is $0.00290 \mathrm {~m} \cdot \mathrm { K }$ ) (a) $400 ^ { \circ } \mathrm { C }$ ? (b) $800 ^ { \circ } \mathrm { C }$ ? (c) $1200 ^ { \circ } \mathrm { C }$ ?

A hydrogen atom makes a downward transition from the $n = 15$ state to the $n = 5$ state. Find the wavelength of the emitted photon. $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right.$ )

Calculate the orbital Bohr radius of the $n = 2$ excited state in a hydrogen atom. $\left( r _ { 1 } = 0.0529 \mathrm {~nm} \right)$

A neutral boron atom has 5 electrons, but in this case all but one of its electrons have been knocked off. How much energy (in electron-volts) is needed to remove the last electron?

What would be the de Broglie wavelength for $1 - \mathrm { g }$ object moving at the earth's escape speed 25,000 mph (about $11 \mathrm {~km} / \mathrm { s } )$ ? $\left( h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

What is the surface temperature of a star, if its radiation peak occurs at a frequency of $1.06 \times 10^{15}$ $\mathrm { Hz }$ ? $\left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right.$ , and the constant in Wien's law is $\left. 0.00290 \mathrm {~m} \cdot \mathrm { K } \right)$

A proton has a speed of $7.2 \times 10 ^ { 4 } \mathrm {~m} / \mathrm { s }$ . What is the energy of a photon that has the same wavelength as the de Broglie wavelength of this proton? $\left( m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , c = 3.00 \times \right.$ $\left. 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

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

What is the wavelength of the matter wave associated with a $0.50 - \mathrm { kg }$ ball moving at $25 \mathrm {~m} / \mathrm { s }$ ? $( h =$ $\left. 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

A helium-neon laser emits light at $632.8 \mathrm {~nm}$ . If the laser emits $1.82 \times 1017$ photons/second, what is its power output in $\mathrm { mW } ? \left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

A hydrogen atom is excited to the $n = 9$ level. Its decay to the $n = 6$ level detected in a photographic plate. What is the frequency of the light photographed? $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \right.$ . s)

When light of wavelength $350 \mathrm {~nm}$ is incident on a metal surface, the stopping potential of the photoelectrons is $0.500 \mathrm {~V}$ . What is the threshold (cutoff) frequency of this metal? $\left( c = 3.00 \times 10 ^ { 8 } \right.$ $\mathrm { m } / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )

When a metal is illuminated by light, photoelectrons are observed provided that the wavelength of the light is less than $520 \mathrm {~nm}$ . What is the metal's work function? ( $c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times$ $10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )