Question

An electron beam has a kinetic energy equal to 100 eV. Find its wavelength associated with a beam, if mass of electron $=9.1\times {10}^{-31}\text{kg}$ and $1\text{eV}=1.6\times {10}^{-19}\text{V}$. (Planck’s constant $=6.6\times {10}^{-34}\text{Js}$)

• A. $24.6\stackrel{\circ }{A}$
• B. $0.12\stackrel{\circ }{A}$
• C. $1.2\stackrel{\circ }{A}$
• D. $6.3\stackrel{\circ }{A}$

Answer 1

The correct option is C

$1.2\stackrel{\circ }{A}$

Here $\text{K}=100\text{eV}=1.6\times {10}^{-17}\text{J}$

$\lambda =\frac{h}{\sqrt{2mK}}=\frac{6.6\times {10}^{-34}}{\sqrt{2\times 9.1\times {10}^{-31}\times 1.6\times {10}^{-17}}}\text{m}$

$=1.22\times {10}^{-10}\text{m}=1.22\stackrel{\circ }{A}$