AP Physics 2 Unit 6: Modern Physics

According to special relativity, a muon traveling at $v=0.99c$ relative to Earth has a lifetime measured in Earth's frame that is longer than its proper lifetime. This phenomenon is called:

The half-life of a radioactive isotope is $T_{1/2}=5\mathrm{days}$. Starting with $N_0=1600$ atoms, how many remain after $20\mathrm{days}$?

A photon has a wavelength of $\lambda =400\mathrm{nm}$. What is its energy in electron-volts? ($h=6.63\times 10^{-34}\mathrm{J}\cdot \mathrm{s}$, $c=3\times 10^{8}m/s$, $1\mathrm{eV}=1.6\times 10^{-19}\mathrm{J}$)

In the Compton effect, an X-ray photon of wavelength ${\lambda }_0$ scatters off a free electron and the scattered photon has a longer wavelength ${\lambda }^{\prime }$. The Compton shift $\Delta \lambda ={\lambda }^{\prime }-{\lambda }_0$ depends on:

In the Bohr model of hydrogen, an electron transitions from energy level $n=3$ to $n=1$. This transition results in:

According to the Heisenberg uncertainty principle, the minimum uncertainty in the momentum of an electron confined to a region of length $\Delta x=1.0\times 10^{-10}\mathrm{m}$ (atomic scale) is approximately: ($h=6.63\times 10^{-34}\mathrm{J}\cdot \mathrm{s}$)

A nuclear reaction fuses two deuterium nuclei to produce helium-3 and a neutron:
$${}_1^2\mathrm{H}+{}_1^2\mathrm{H}\to {}_2^3\mathrm{He}+{}_0^1\mathrm{n}$$
Given that the mass defect is $\Delta m=3.3\times 10^{-30}\mathrm{kg}$, how much energy is released? ($c=3\times 10^{8}m/s$)

Light of frequency $f=1.5\times 10^{15}\mathrm{Hz}$ illuminates a metal with work function $\varphi =3.6\mathrm{eV}$. What is the maximum kinetic energy of the emitted electrons in eV? ($h=4.14\times 10^{-15}\mathrm{eV}\cdot \mathrm{s}$)

In the photoelectric effect, which property of light determines the maximum kinetic energy of the ejected electrons?

In nuclear physics, a nucleus with mass number $A=235$ and atomic number $Z=92$ (uranium-235) undergoes alpha decay. What are the mass number and atomic number of the daughter nucleus?

A particle is accelerated through a potential difference of $V=50\mathrm{kV}$. Using the de Broglie relation $\lambda =h/p$ and energy conservation (non-relativistic), what is the de Broglie wavelength of a proton accelerated through this potential? ($m_p=1.67\times 10^{-27}\mathrm{kg}$, $e=1.6\times 10^{-19}\mathrm{C}$, $h=6.63\times 10^{-34}\mathrm{J}\cdot \mathrm{s}$)

The de Broglie wavelength of a particle with momentum $p$ is given by: