(a)What is de Broglie's hypothesis? Derive an expression for the matter wavelength using de Broglie's hypothesis.A photo

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(a)What is de Broglie's hypothesis? Derive an expression for thematter wavelength using de Broglie's hypothesis.A photon of 1 MeVcollides with a free but stationary electron and scatters off at anangle 90°. What are the energies of the scattered photon and thekinetic energy of the recoil electron?(b)A nuclear reactor uses 92U238 tocreate a power level of 300 MW. Calculate the rate of consumptionof 92U238 per year. Given that theenergy released per fission of 92U238 is200 MeV and mass of each nucleon is equal to 1 a.m.u. = 1.66 x1O-27kg.(c) Define torque. State the principle of the conservation ofangular momentum. Show that the relation L =I where I ismoment of inertia and is angularvelocity.(d)Derive Bernoulli's equation for a fluid in streamlinemotion.Calculate the speed at which the velocity head of a streamof water is equal to 0.50 m of Hg.(e)Write down the time-independent Schrodinger equation for aparticle moving in a potential V. Consider a particle moving freelyin a one-dimensional box of length D. The potential energy of theparticle may be expressed as Determine its energy eigenvalue and normalized wave function.(f)Find the probability current density carried by a planewave (x)=Aeikx inone dimension.