Problem 1.1 Calculate the de Broglie wavelength of an electron moving at 2.5 × 10⁶ m/s. Compare this to the wavelength of a photon with the same momentum.
Problem 1.2 A photon has a wavelength of 550 nm (green light). Find its: (a) frequency (b) energy in joules (c) energy in eV (d) momentum
Problem 1.3 An electron is accelerated from rest through a potential difference of 100 V. Calculate: (a) its kinetic energy in eV (b) its de Broglie wavelength (c) its speed (non-relativistic approximation is acceptable)
Problem 1.4 For a relativistic electron with total energy E = 2.0 MeV: (a) Find the kinetic energy (b) Calculate the momentum using equation 1-3 (c) Determine the de Broglie wavelength (d) Find the speed using equation 1-5
Problem 1.5 A helium-neon laser emits light at wavelength 632.8 nm with a power of 5.0 mW. How many photons does it emit per second?
Problem 1.6 Compare the energy and momentum of: (a) A 1.0 MeV photon (b) A 1.0 MeV electron (total energy) Which has the shorter wavelength?
Problem 1.7 An X-ray photon has energy 50 keV. Calculate: (a) its wavelength (b) its momentum (c) the momentum of an electron with the same energy
Problem 1.8 The average wavelength of sunlight is approximately 550 nm, and the solar constant (irradiance at Earth’s distance) is 1360 W/m². Calculate: (a) the energy per photon (b) the number of photons per square meter per second reaching Earth’s atmosphere
Problem 1.9 A microwave oven operates at frequency 2.45 GHz. Find: (a) the wavelength (b) the photon energy in joules and eV (c) the number of photons emitted per second if the oven generates 800 W of microwave power
Problem 1.10 An AM radio station broadcasts at 1200 kHz with a power of 50 kW. An FM station broadcasts at 101.5 MHz with the same power. Calculate the number of photons per second emitted by each station and comment on the detectability of individual photons.