Show the unit of `h/(mv)` is equal to that of wavelength.

A calorie is a unit of heat or energy and it equals about 4.2 j where 1 J = 1 kg . m^(2). S^(-2) . Suppose we employ a system of units in which the unit of mass equals alpha kg the unit of length equals beta m and the unit of time is lambda s. Show the a calorie has a magnitude 4.2 alpha^(-1) beta^(-2) gamma^(2) in terms of the new units.

The de Broglie wavelength of an electron moving with a velocity c/2 (c =velocity of light in vacuum) is equal to the wavelength of a photon. The ratio of the kinetic energies of electron and photon is

Show the dimension of L/R is equal to the dimension of time.

The wavelength of photon of lambda is equal to the de-Broglie wave length of electron. Show that energy of photon =2lambdamc/hxx kinetic energy of electron .

Considering the earth as a uniform sphere of radius R show that if the acceleration due to gravity at a height h from the surface of earth is equal to the acceleration due to gravity at the same depth, then h=1/2(sqrt(5)-1)R.

Considering the earth as a uniform sphere of radius R show that if the acceleration due to gravity at a height h from the surface of earth is equal to the acceleration due to gravity at the same depth, then h= 1/2(sqrt5-1) R

1 BOT unit is equal to

Show that the unit of 'PV' is the unit of work or energy.

The wavelength associated with a photon and the de Broglie wavelength of a moving electron are equal. If they carry the same amount of energy, what is the value of this wavelength?