An electron and a proton each have kinetic energy equal to 50 keV. (a) What are their de Broglie wavelengths? (b) Which one can be used to see a smaller feature (or object)? (c) What are the potential applications of such energetic particles?

Consider an electron with a (non-relativistic) kinetic energy of 1 eV. (i) What is the electron speed in m/s? What is the de Broglie wavelength of the electron? (ii) Consider a beam of 1 eV electrons incident on a pair of very thin slits, separated by a distance d, with an interference pattern seen on a screen 2 m beyond the slits. Find the value of d such that the position of the first off-center bright fringe of the pattern is located 0.5mm from the center of the pattern.

In a photoelectric experiment it is found that a stopping potential of 1.00 V is needed to stop all the electrons when incident light of wavelength 264 nm is used and 2.3 V is needed for light of wavelength 207 nm. From these data determine Planck's constant. (Enter your answer, in eV · s, to at least four significant figures.) eV s From these data determine the work function (in eV) of the metal. eV

(a) A vacuum photocell is sequentially illuminated with light of different wavelengths 2. A voltmeter is used to determine that there is a different voltage between the cathode and the anode. V (iii) Determine a relation for Planck's constant in terms of pairs of voltage measurements at different wavelengths such that W₁ cancels out. (iv) Evaluate Planck's constant for the following pair of measurements: measurement 1 finds = 447 nm and V=635 mV, and measurement 2 finds = : 502 nm and V=339 mV.