Using de Broglie's relation derive E=n2h2/8mL . Given the wavelength of the particle is λ=2L/n, where...
Using de Broglie's relation derive E=n2h2/8mL . Given the wavelength of the particle is λ=2L/n, where the particle's wavelength is shown in terms of the length of the box for the nth level.
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Using de Broglie's relation derive
E=n2h2/8mL . Given the wavelength of the
particle is λ=2L/n, where...
need help with I-K I. The de Broglie wavelength for a baseball (100 g) traveling at 40 m/s is (a) 1.6x103 m (b) 3.3x10-34 m (c) 1.6x1024 nm (b) 3.3x1024 m Questions J and K refer to butadiene, C4H...
need help with I-K
I. The de Broglie wavelength for a baseball (100 g) traveling at 40 m/s is (a) 1.6x103 m (b) 3.3x10-34 m (c) 1.6x1024 nm (b) 3.3x1024 m Questions J and K refer to butadiene, C4Hs (4 carbon with 2 double bonds), a t electron system that can be studied using the particle-in-a-box model, and the allowed energies are given by n-4 n 3 n 1,2,3 En- n- 1 where L is the length of the box...
(ii) The quantised energies of a particle in a two-dimensional square box are given by: where a i...
(ii) The quantised energies of a particle in a two-dimensional square box are given by: where a is the length of the box in each dimension. Obtain expressions for the particle's energy for nı = 1 and n-= 3, and for nı = 3 and n-=1. Comnnment on the results. 121
(ii) The quantised energies of a particle in a two-dimensional square box are given by: where a is the length of the box in each dimension. Obtain expressions for...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can'...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
2, 2L 3 cantilever beam shown ttnd. : (a) the angles of rotation e, de S α+ A ^n B (vnaj aud direc of each) (b) the maximum deflection S , and where it ‘eers(the value of Use the neod of Saee interra...
2, 2L 3 cantilever beam shown ttnd. : (a) the angles of rotation e, de S α+ A ^n B (vnaj aud direc of each) (b) the maximum deflection S , and where it ‘eers(the value of Use the neod of Saee interratiens, starting fiom the bending a n moment eguafion
2, 2L 3 cantilever beam shown ttnd. : (a) the angles of rotation e, de S α+ A ^n B (vnaj aud direc of each) (b) the maximum deflection...
a) Discuss why the de Broglie wavelength λ corresponding to a momentum p (p wavenumber given...
a) Discuss why the de Broglie wavelength λ corresponding to a momentum p (p wavenumber given by k # 2n/A) leads to a representation of p by the operator p as (h/) (d/dx) hk, where k is the b) Using theoperao orm of p given in part a, show that,pih c) The total energy of a simple harmonic oscillator of mass M and spring constant K can be written as H- p2/M + ke . If the mass is displaced...
When monochromatic light of wavelength 500 nm is shown on a certain metal, el 1. are...
When monochromatic light of wavelength 500 nm is shown on a certain metal, el 1. are emitted with energy of 1.20 electron volts. a) How much energy was required to remove the electron from the metal? b What-is-the-de-Broghie wavelength ot the emitied oleetrons? het Flesti Soo 2. An electron is in box of length L, and is not allowed outside the box, so y 0 exc 0sxs L. The wavefunction for the electron is found to be Ψ(x)-Asin(kx). a) Use...
The eigenfunctions for a particle in a one-dimensional box of length L, and the corresponding energy...
The eigenfunctions for a particle in a one-dimensional box of length L, and the corresponding energy eigenvalues are given below. What is the variance of measurements for the linear momentum, i.e., Op = v<p? > - <p>2? Øn (x) = ( )" sin nga, n= 1, 2,.. En = n2h2 8m12 Note the Hamiltonian operator to give the energy is H = = - 42 8n72 dx2 nh 2L oo O nềh2 412 Uncertain since x is known. Following Question...
What is the de Broglie wavelength (in meters) of a neutron traveling at a speed of...
What is the de Broglie wavelength (in meters) of a neutron traveling at a speed of 0.92 c? Since the neutron's speed is close to the speed of light (c), Special Relativity must be used when calculating the linear momentum (p). The mass of the neutron is 1.675 x 10-27 kg. Suppose that an alpha particle (mαα = 6.646 x 10-27 kg) has a kinetic energy of 75 keV. What is the alpha particle's speed (v) (in terms of "c")?...
Recall that for the Harmonic oscillator: vmk h Where k 2/2 is the wavenumber and m is the particle mass. =n2R-2k (n-2k...
Recall that for the Harmonic oscillator: vmk h Where k 2/2 is the wavenumber and m is the particle mass. =n2R-2k (n-2k)!k HT ka-2k where a integers; the coresponding wavefuction is Where k and |n are = The first three solutions (lecture 3) for the quantum harmonic oscillator are: n 0,k 0 Ho(1 = hwo/2 = ' Eo 25 E, — Зho/2 Н. (€) n 1, k n 2, k 0,1 E2 5hao/2 H2(42 2, Plot for a 1 ev...
1. Imagine a version of the particle in a box where the potential is given by:...
1. Imagine a version of the particle in a box where the potential is given by: b-1 b-1 oootherwise where b is any real number greater than or equal to 2 a) Assuming that > Vo for all n, use the WKB approximation to find the energies. Give your final answer in terms of b, b, and E b) What happens in either extreme, as b approaches 2 or o°? Does the WKB approximation give the exact answers in these...
need help with I-K
I. The de Broglie wavelength for a baseball (100 g) traveling at 40 m/s is (a) 1.6x103 m (b) 3.3x10-34 m (c) 1.6x1024 nm (b) 3.3x1024 m Questions J and K refer to butadiene, C4Hs (4 carbon with 2 double bonds), a t electron system that can be studied using the particle-in-a-box model, and the allowed energies are given by n-4 n 3 n 1,2,3 En- n- 1 where L is the length of the box...
(ii) The quantised energies of a particle in a two-dimensional square box are given by: where a is the length of the box in each dimension. Obtain expressions for the particle's energy for nı = 1 and n-= 3, and for nı = 3 and n-=1. Comnnment on the results. 121
(ii) The quantised energies of a particle in a two-dimensional square box are given by: where a is the length of the box in each dimension. Obtain expressions for...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
2, 2L 3 cantilever beam shown ttnd. : (a) the angles of rotation e, de S α+ A ^n B (vnaj aud direc of each) (b) the maximum deflection S , and where it ‘eers(the value of Use the neod of Saee interratiens, starting fiom the bending a n moment eguafion
2, 2L 3 cantilever beam shown ttnd. : (a) the angles of rotation e, de S α+ A ^n B (vnaj aud direc of each) (b) the maximum deflection...
a) Discuss why the de Broglie wavelength λ corresponding to a momentum p (p wavenumber given by k # 2n/A) leads to a representation of p by the operator p as (h/) (d/dx) hk, where k is the b) Using theoperao orm of p given in part a, show that,pih c) The total energy of a simple harmonic oscillator of mass M and spring constant K can be written as H- p2/M + ke . If the mass is displaced...
When monochromatic light of wavelength 500 nm is shown on a certain metal, el 1. are emitted with energy of 1.20 electron volts. a) How much energy was required to remove the electron from the metal? b What-is-the-de-Broghie wavelength ot the emitied oleetrons? het Flesti Soo 2. An electron is in box of length L, and is not allowed outside the box, so y 0 exc 0sxs L. The wavefunction for the electron is found to be Ψ(x)-Asin(kx). a) Use...
The eigenfunctions for a particle in a one-dimensional box of length L, and the corresponding energy eigenvalues are given below. What is the variance of measurements for the linear momentum, i.e., Op = v<p? > - <p>2? Øn (x) = ( )" sin nga, n= 1, 2,.. En = n2h2 8m12 Note the Hamiltonian operator to give the energy is H = = - 42 8n72 dx2 nh 2L oo O nềh2 412 Uncertain since x is known. Following Question...
Recall that for the Harmonic oscillator: vmk h Where k 2/2 is the wavenumber and m is the particle mass. =n2R-2k (n-2k)!k HT ka-2k where a integers; the coresponding wavefuction is Where k and |n are = The first three solutions (lecture 3) for the quantum harmonic oscillator are: n 0,k 0 Ho(1 = hwo/2 = ' Eo 25 E, — Зho/2 Н. (€) n 1, k n 2, k 0,1 E2 5hao/2 H2(42 2, Plot for a 1 ev...
1. Imagine a version of the particle in a box where the potential is given by: b-1 b-1 oootherwise where b is any real number greater than or equal to 2 a) Assuming that > Vo for all n, use the WKB approximation to find the energies. Give your final answer in terms of b, b, and E b) What happens in either extreme, as b approaches 2 or o°? Does the WKB approximation give the exact answers in these...
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