PHYSICS F/SCI.+ENGR.,V.1 (CHAP.1-20)
5th Edition
ISBN: 9780134378053
Author: GIANCOLI
Publisher: RENT PEARS
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Chapter 37, Problem 45P
To determine
The speed of the neutrons for the given conditions.
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(i) Is an electron a particle? Is it a wave? Explain your answer citing relevant experimental evidence. Calculate the De-Broglie wavelength of an electron having a kinetic energy of 1000eV. Compare the result with wavelength of X-rays having the same energy.
(10) i) Use the quantum mechanical kinetic energy operator T, =
to find the kinetic energy of the first
2m dx?
excited state of the Particle in a Box (with n = 2). ii) Then, use the relationship of kinetic energy and momentum (KE
= p?/2m) to find an equation for the de Broglie wavelength of the particle in a one-dimensional box as a function only
of the box length L and quantum number n. iii) Sketch the wavefunction in the box to verify that the expression you
obtained in part ii) is correct.
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.
Chapter 37 Solutions
PHYSICS F/SCI.+ENGR.,V.1 (CHAP.1-20)
Ch. 37 - Prob. 1QCh. 37 - Prob. 2QCh. 37 - Prob. 3QCh. 37 - Prob. 4QCh. 37 - Prob. 5QCh. 37 - Prob. 6QCh. 37 - Prob. 7QCh. 37 - Prob. 8QCh. 37 - Prob. 9QCh. 37 - Prob. 10Q
Ch. 37 - Prob. 11QCh. 37 - Prob. 12QCh. 37 - Prob. 13QCh. 37 - Prob. 14QCh. 37 - Prob. 15QCh. 37 - Prob. 16QCh. 37 - Prob. 17QCh. 37 - Prob. 18QCh. 37 - Prob. 19QCh. 37 - Prob. 20QCh. 37 - Prob. 1PCh. 37 - Prob. 3PCh. 37 - Prob. 7PCh. 37 - Prob. 9PCh. 37 - Prob. 13PCh. 37 - Prob. 25PCh. 37 - Prob. 26PCh. 37 - Prob. 27PCh. 37 - Prob. 32PCh. 37 - Prob. 34PCh. 37 - Prob. 37PCh. 37 - Prob. 45PCh. 37 - Prob. 52PCh. 37 - Prob. 76GPCh. 37 - Prob. 77GP
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- (i) Show that the classical Rayleigh-Jeans formula is a special case of Planck's radiation formula. (ii) Given a wave function of a particle as = Ae-ip/hy, confined such that 0arrow_forwardThe velocity of a neutron is measured to be 6.0 x 106 m s-1 with an uncertainty of 1.0 × 103 m s-1. (i) What is the minimum uncertainty of the simultaneous measurement of the position of the neutron? (ii) State how the minimum uncertainties of a measured energy and a measured time are relatedarrow_forward(c) Light of wavelength 450 nm is emitted by an electron in an atom behaving as a lightly damped simple harmonic oscillator with a Q value of 2×107. Find the natural frequency of the system in radians per second.arrow_forward(a) If the wavelength of an electron is 4.70 × 10- m, how fast is it moving? km/s (b) If the electron has a speed equal to 2.30 x 10° m/s, what is its wavelength? marrow_forward(b) (i) Calculate the de Broglie wavelength of an electron having a mass of 9.11 x 1031 kg and a charge of 1.602 x 10-19 J with a Kinetic energy of 135 eV. The value of the Planck's constant is equal to 6.63 * 10-34 Js. (ii) Assume that an electron is moving along the x-axis with a speed of 3.66 x 106 m/s and with a precision of 0.50%. Calculate the minimum uncertainty (as allowed by the uncertainty principle in quantum theory) with which the position of the electron along the X-axis simultaneously can be measured with the speed?arrow_forward(c) Light of wavelength 550 nm falls on the surface of metal of work function 3.5 eV. (i) Calculate the maximum kinetic energy of the electrons emitted Calculate the cut-off frequency. (ii)arrow_forwardThe resolving power of a microscope depends on the wavelength used. If you wanted to “see” an atom, a wavelength of approximately 1.00 × 10-11 m would be required. (a) If electrons are used (in an electron microscope), what minimum kinetic energy is required for the electrons? (b) What If? If photons are used, what minimum photon energy is needed to obtain the required resolution?arrow_forwardTyped onlyarrow_forwardResolving ‘power’ of an electron microscope versus optical (photon) microscope: If a resolution of 1.0 x 10-11m (0.010nm) is required to ‘see’ an atom, (a) If electrons are used (e-microscope), what minimum kinetic energy of the electrons is required? Use deBroglie’s Hypothesis and KE = p2/2me and non-relativistic velocities: (b) If photons are used, what minimum KE (Eγ) is required to obtain 10-11m resolution?arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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