Question

Derive between Kinetic energy and wavelength of a moving particle​

Answer 1

Explanation:

The kinetic energy of the electrons accelerated through a potential difference (voltage) V was E = ½mv2 = p2/(2m) = eV and the de Broglie formula then yields λ = h/(2meV)1/2, where e and m are the charge and the mass of the electron respectively.

Answer 2

According to De Broglie’s equation, wavelength=h/mv.

Now lets find relation between mv and kinetic energy,

y=mv

y^2=m(mv^2)

(y^2)/2=m(1/2mv^2)

(y^2)/2=mKE [as KE=(1/2mv^2)]

hence, y=(2mKE)^(1/2)=mv

Now we can easily see that,

Wavelength=h/(2mKE)^(1/2)

This is the mathematical relation between Kinetic energy and wavelength.

Hope it helps you