2. To "observe" small objects, one measures the diffraction of particles whose de Broglie wavelength is approximately equal to the object's size. Find the kinetic energy (in electron volts) required for electrons to resolve (a) a large organic molecule of size 10.0 nm, (b) atomic features of size 0.100 nm, and (c) a nucleus of size 10.0 fm.
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- 73. When a metal is illuminated with light of wavelength 420 nm, the stopping potential is 0.65 V; when the wavelength of incident light is changed to 310 nm, the stopping potential is 1.69 V. Use these given data to find the work function of this metal in eV and a value of Planck's constant h (speed of light = 3 × 10® m/s, electronic charge = -1.6 x 10-19 C).1. Louis de Broglie postulated all matter has both a particle and wave nature. The wavelength of any matter wave is given by λ = h/p, where p is the linear momentum p = mv and both p and v are vectors. a) World class marathon runners can run at an average pace of about 3.00 min/km. What is the wavelength, momentum and kinetic energy of a 55 kg runner racing at this average speed? b) What is the uncertainty in the runner's velocity if the position is to be determined within one wavelength?
- 8. Caesium has a work function of 2.1 eV. If the wavelength of light 2 is 450 nm, calculate the (a) maximum kinetic energy (b) stopping potential (c) threshold frequency1. Find the shortest and longest wavelengths present in the Paschen series.(15/100)2. Find the quantum number that characterizes the earth’s orbit around the sun.The earth’s mass is 6.0 × 10 24 kg, its orbital radius is 1.5 × 10 11 m, and its orbitalspeed is 3.0 × 10 4 m/s. (15/100)3. How much energy is required to remove an electron in the n = 2 state from ahydrogen atom? (15/100)Values for certain constants:h = 6.626 × 10 −34 Js, E 1 = −13.6 eV, r 1 = 5.29 × 10 −11 m, 1 eV = 1.602 × 10 −19 J.4. What is the maximum acceleration potential (V) must be applied to electrons to cause electron diffraction on (220) planes of Lithium at 0 = 5°? (aLi = 3.517A°, m. = 9.1093837015 × 10' kg, q. = 1.6 × 10-19 coulomb, h = 6.62 x 10 34 J.S).
- 51) A photon of energy 1.24 eV is absorbed by a molecule. a) What is its wavelength in cm and the reciprocal of its wavelength in cm-1? A..........cm B..........cm-1 The molecule transitions to an energy level of 0.24 eV, and emits a photon. b) What is the energy of the emitted photon (eV)? ..........eV c) What is its wavelength in cm and the reciprocal of its wavelength in cm-1? C..........cm D..........cm-1 d) Find D-B in cm-1. ..........cm-1 The second photon of energy 1.14 eV is absorbed by the same molecule. e) What is its wavelength in cm and the reciprocal of its wavelength in cm-1? E..........cm F..........cm-1 The molecule transitions to an energy level of 0.24 eV, and emits a photon. f) What is the energy of the emitted photon (eV)? ..........eV g) What is its wavelength in cm and the reciprocal of its wavelength in cm-1? G..........cm…7) Find the wavelength of the photon as an electron makes a transition from n=4 to n=3. for particle in a box with E1=13.6 eV1. A free electron has the wavefunction p(x, t) = sin(kx – wt) and wave number k = 50nm-1 1.1 Determine the electron's de Broglie wavelength. 1.2 Determine the electron's momentum. 1.3 Determine the electron's kinetic energy. 2. An electron is trapped in an infinite potential well of width 1 cm. For what value of n will electron have an energy of 2 eV? 3. Give the Born interpretation of the wavefunction.
- 4. An electron has a momentum py =1.30 x 10 kg.m/s. What is the minimum uncertainty in its position that will keep the relative uncertainty in its momentum (Apy/p) below 2.3%? (35.3 nm3. Find the energy of the scattered photon, the electron's kinetic energy, and Compton's shift of a wavelength of 0.01 Å when scattering at angle 70° where: h = 6.62×1034 & mo = 9.11×1031 & c = 3x108 4. Find the positron scattering angle, if the incident photon has frequency 3x 1022 Hz where: h = 6.62x1034 & mo = 9.11×10-31 & c = 3x1085. What are the kinetic energy and the speed of an electron ejected from a sodium surface whose work function is W0 = 2.28 eV when illuminated by light of wavelength (a) 410 nm and (b) 550 nm?