Chapter 7, Problem 7A.3ST

Interpretation Introduction

Interpretation:

The electron wavelength in $\text{10}\text{MeV}$ accelerator has to be calculated.

Concept Introduction:

Work function: Work function of a metal is measure of strength of electrons is held in a metal atom.

$\text{hν}\text{=}\text{KE}\text{+}\varphi \boxed{\begin{array}{c}here,\varphi =\text{ work function}\\ \text{KE }=\text{ kinetic energy}\\ \text{h = Planck’s constant} \\ \text{ν}=\text{ frequency}\end{array}}$

Energy can be in the form of kinetic energy or potential energy.  Kinetic energy is the energy associated with motion.

${\text{E}}_{\text{k}}\text{=}\frac{\text{1}}{\text{2}}{\text{mv}}^{\text{2}}\boxed{\begin{array}{l}here,\text{m - Mass in kilograms}\hfill \\ \text{v - Velocity in meters per second}\hfill \end{array}}$

Louis de Broglie in $1923$ rationalized that when light shows particle aspects, then particles of matter display properties of waves under definite circumstances.

$\begin{array}{c}\text{λ}\text{=}\frac{\text{h}}{\text{m}\text{υ}}\\ \text{p = m}\text{υ}\\ \text{Hence λ}\text{=}\frac{\text{h}}{\text{p}}\\ \boxed{\begin{array}{l}\text{h is Planck’s constant }\left(6.626\times {10}^{-34}\text{J}\text{.s}\right)\text{ which relates energy and frequency}\\ \text{υ}\text{is the speed of particle}\\ \text{m is the mass of particle }\\ \text{λ}\text{is the wavelength}\\ \text{p is the momentum}\end{array}}\end{array}$

The above equation is called de Broglie relation.