Exam 39: Particles Behaving As Waves

A nonrelativistic electron is confined to a length of 500 pm on the x-axis.What is the kinetic energy of the electron if its speed is equal to the minimum uncertainty possible in its speed? ,m_el = 9.11 × 10^-31 kg,1 eV = 1.60 × 10^-19 J)

At absolute temperature T,a black body radiates its peak intensity at wavelength λ.At absolute temperature 2T,what would be the wavelength of the peak intensity?

The lifetime of an excited nuclear state is 1.0 ns.What is the minimum uncertainty in the energy of this state? ( h = 1.055 × 10^-34 J • s = 6.591 × 10^-16 eV • s,

In the vicinity of what frequency does an object with a temperature of 1000 K radiate the largest amount of power? (c = 3.00 × 10⁸ m/s,Wien displacement law constant equals ,σ = 5.670 × 10^-8 W/m² • K⁴)

A collection of atoms has 20% of the sample in a state above the ground state.If these emit coherent radiation,what is the wavelength of the laser light produced? ,h = 6.626 × 10^-34 J ∙ s,1 eV = 1.60 × 10^-19 J)

A single slit is illuminated at normal incidence with a parallel beam of light having a wavelength of The entire central band of the diffraction pattern is observed at ±90°.The illumination is now replaced by a nonrelativistic beam of electrons,each having a kinetic energy of 980 eV.When this beam hits the slit at normal incidence,at what angle will the first minimum of the electron diffraction pattern occur? (h = 6.626 × 10^-34 J • s, ,1 eV = 1.60 × 10^-19 J)

A hydrogen atom is excited to the n = 10 stated.It then decays to the n = 4 state by emitting a photon which is detected in a photographic plate.What is the frequency of the detected photon? The lowest level energy state of hydrogen is -13.6 eV.(h = 6.626 × 10^-34 J ∙ s,

A nonrelativistic electron and a nonrelativistic proton have the same de Broglie wavelength.Which of the following statements about these particles are accurate? (There may be more than one correct choice.)

A small dust particle of mass 7.90 × 10^-6 g is being observed under a magnifying lens.Its position is determined to within 0.0050 mm.(1 y = 3.156 × 10⁷ s, (a)Find the minimum uncertainty in its velocity implied by the uncertainty in its position. (b)Assuming the dust particle is moving at the speed you just found,how many years would it take for the particle to move 1.0 mm?

The excited state of a certain atom is 3.2 eV ± 0.21 eV.( h = 1.055 × 10^-34 J • s = ,1 eV = 1.60 × 10^-19 J) (a)What is the average lifetime of this state? (b)If the excited energy were doubled to 6.4 eV ± 0.21 eV,how would the lifetime be affected?

Light of wavelength 105 nm falls on a metal surface for which the work function is 5.00 eV.What is the minimum de Broglie wavelength of the photoelectrons emitted from this metal? (h = 6.626 × 10^-34 J • s = 4.14 × 10^-15 eV • s,c = 3.00 × 10⁸ m/s, ,

You need 14 W of infrared laser light power with wavelength 1270 nm to bore a hole in a diamond.How many downward atomic transitions per second must occur in the laser if all of them result in light directed onto the diamond? (c = 3.00 × 10⁸ m/s,h = 6.626 × 10^-34 J • s)