35. Special Relativity

The probe passes over an atom that is 0.050 nm “tall.” By what factor does the tunneling current increase?

Identify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state. 1s² 2s² 2p⁵

A pi meson of mass m_π decays at rest into a muon (mass m_μ) and a neutrino of negligible or zero mass. Show that the kinetic energy of the muon is K_μ = (m_π - m_μ)² c² / (2m_π).

A proton’s energy is 1.0 MeV below the top of a 10-fm-wide energy barrier. What is the probability that the proton will tunnel through the barrier?

To initiate a nuclear reaction, an experimental nuclear physicist wants to shoot a proton into a 5.50-fm-diameter ¹²C nucleus. The proton must impact the nucleus with a kinetic energy of 3.00 MeV. Assume the nucleus remains at rest. Through what potential difference must the proton be accelerated from rest to acquire this speed?

The shortest visible wavelength is about $400$ nm. What is the temperature of an ideal radiator whose spectral emittance peaks at this wavelength?

Estimate the speed of a galaxy, and its distance from us, if the wavelength for the hydrogen line at 434 nm is measured on Earth as being 625 nm.

55 keV x-ray photons are incident on a target. At what scattering angle do the scattered photons have an energy of 50 keV?

While undergoing a transition from the $n=1$ to the $n=2$ energy level, a harmonic oscillator absorbs a photon of wavelength $6.50$ $\mu$m. What is the wavelength of the absorbed photon when this oscillator undergoes a transition (a) from the $n=2$ to the $n=3$ energy level and (b) from the $n=1$ to the $n=3$ energy level?

(c) What is the value of $\sqrt{\left(k^{\prime }/m\right)}$, the angular oscillation frequency of the corresponding Newtonian oscillator?

During what interval of time will 10% of a sample of 2p hydrogen atoms decay?

Two protons, each having a speed of 0.945c in the laboratory, are moving toward each other. Determine (a) the momentum of each proton in the laboratory, (b) the total momentum of the two protons in the laboratory, and (c) the momentum of one proton as seen by the other proton.