Question

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

• A. $ 6.3\,\mathring{A}$
• B. $ 3.8\,\mathring{A}$
• C. $ 24.6\,\mathring{A}$
• D. $ 0.12\,\mathring{A}$

Answer 1

Answer: (B)

de-Broglie's wavelength associated with a charged particle, $\lambda=\frac{h}{\sqrt{2 m K E}}$
$=\frac{6.6 \times 10^{-34}}{\sqrt{2 \times 9.1 \times 10^{-31} \times 10 \times 1.6 \times 10^{-19}}}=3.8 \,\mathring{A}$