Exam 27: Early Quantum Theory and Models of the Atom

If an electron has a wavelength of $0.123 \mathrm {~nm}$ , what is its kinetic energy, in electron-volts? This energy is not in the relativistic region. ( $m$ electron $= 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , h = 6.626$ $\times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s }$ )

In a hydrogen atom, the electron makes a transition from the $n = 8$ to the $n = 3$ state. The wavelength of the emitted photon is closest to which one of the following values? $\left( c = 3.00 \times 10 ^ { 8 } \right.$ $\mathrm { m } / \mathrm { s } , 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s }$ )

A person of mass $50 \mathrm {~kg}$ has a de Broglie wavelength of $4.4 \times 10 ^ { - 36 } \mathrm {~m}$ while jogging. How fast is she running? $\left( h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

If the wavelength of a light beam is doubled, what happens to the momentum of the photons in that light beam?

Gamma rays are photons with very high energy. How many visible-light photons with a wavelength of $500 \mathrm {~nm}$ would you need to equal the energy of a gamma-ray photon with energy $4.1 \times 10 ^ { - 13 } \mathrm {~J}$ ?

In making a transition from state $n = 1$ to state $n = 2$ , the hydrogen atom must

What is the cutoff (threshold) frequency for a metal surface that has a work function of $5.42 \mathrm { eV }$ ? (1 $\left. \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

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

Two sources emit beams of microwaves. The microwaves from source A have a frequency of 10 GHz, and the ones from source B have a frequency of 20 GHz. 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.)

A 29.0-pm-wavelength photon is scattered by a stationary electron. What is the maximum energy Ioss the photon can have? ( $m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } , 1$ $\mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J}$ )

A hydrogen atom is in its $n = 2$ excited state when its electron absorbs $9.5 \mathrm { eV }$ in an interaction with a photon. What is the energy of the resulting free electron?

As the temperature of a blackbody increases, what happens to the peak wavelength of the light it radiates?