(a) Show that for a non-relativistic particle of mass m and kinetic energy K, the de Broglie wavelength is given by, 1 = h/(2mK)"2 1/2 (b) Show that if the particle is moving with a relativistic velocity, the wavelength will be given by, 1= h c/ [K (K+ 2mc³)]², where K is the relativistic kinetic energy. (c) Find approximate expressions for as a function of K in the special cases: (i) K« mc² (non- relativistic limit); and (ii) K>> mc² (extreme-relativistic limit). (d) Çalculate the de Broglie wavelength for a proton with kinetic energy 25 Mev and 7.00 GeV.
(a) Show that for a non-relativistic particle of mass m and kinetic energy K, the de Broglie wavelength is given by, 1 = h/(2mK)"2 1/2 (b) Show that if the particle is moving with a relativistic velocity, the wavelength will be given by, 1= h c/ [K (K+ 2mc³)]², where K is the relativistic kinetic energy. (c) Find approximate expressions for as a function of K in the special cases: (i) K« mc² (non- relativistic limit); and (ii) K>> mc² (extreme-relativistic limit). (d) Çalculate the de Broglie wavelength for a proton with kinetic energy 25 Mev and 7.00 GeV.
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Explain each step plz
![(a) Show that for a non-relativistic particle of mass m and kinetic energy K, the de Broglie
wavelength is given by, 1 = h/(2mK)"2
1/2
(b) Show that if the particle is moving with a relativistic velocity, the wavelength will be given
by, 1= h c/[K (K+ 2mc²)]", where K is the relativistic kinetic energy.
%3D
(c) Find approximate expressions for as a function of K in the special cases: (i) K << mc² (non-
relativistic limit); and (ii) K>> mc² (extreme-relativistic limit).
(d) Calculate the de Broglie wavelength for a proton with kinetic energy 25 Mev and 7.00 GeV.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9397f33b-d5fc-4939-86c6-50211727ada5%2Facdc8321-265b-499a-b84a-60bdec704e8f%2Frqlmu7m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Show that for a non-relativistic particle of mass m and kinetic energy K, the de Broglie
wavelength is given by, 1 = h/(2mK)"2
1/2
(b) Show that if the particle is moving with a relativistic velocity, the wavelength will be given
by, 1= h c/[K (K+ 2mc²)]", where K is the relativistic kinetic energy.
%3D
(c) Find approximate expressions for as a function of K in the special cases: (i) K << mc² (non-
relativistic limit); and (ii) K>> mc² (extreme-relativistic limit).
(d) Calculate the de Broglie wavelength for a proton with kinetic energy 25 Mev and 7.00 GeV.
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