Answers

The Brainliest Answer!
2015-04-29T12:11:13+05:30

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
H = Planck's constant,         p = momentum of electron,        m = mass of electron
v = velocity of electron,          ν = frequency of wave of photon
λ = wavelength of photon        E1 = kinetic energy of electron
E2 = Kinetic energy of photon        c = speed of light

DeBroglie wavelength of electron = λ = h / p
     p = m v  =>    p²  =  2 m E1      =>  p = √(2 m E1)        =>  λ = h /√(2 m E1)
              E1 = h² / (2 λ² m)

Photon
     E2 = h ν = h c /λ            =>        λ = h c /E2

    => E2 / E1 = h c / λ  * 2 λ² m / h²
                     = 2 m c λ / h        
====================
for example
energy of photon to energy of electron with the same wavelength 500 nm
              =  2 * 9.11 * 10⁻³¹ * 3 * 10⁸ * 500 * 10⁻⁹ / 6.636 * 10⁻³⁴
             = 0.008237
================
wavelength of electron :  λ = h / p  = h / m v,        v = velocity of electron

substitute this value in the ratio of energies.

   E2 / E1 = 2 m c λ / h = 2 m c (h / m v) /  h
   =>  E2 / E1  = 2 c / v

2 5 2
ratio in the book is given as v/2c ....why ?
pls see the modification. please click on thanks blue button above.
super . thanks