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 $\left.=6.6 \times 10^{-34} J s\right)$

• A. $24.6 \,\mathring{A}$
• B. $0.12 \,\mathring{A}$
• C. $1.2 \,\mathring{A}$
• D. $6.3 \,\mathring{A}$

Answer 1

Answer: (C)

Kinetic energy $( E )=100 eV$;
Mass of electron $( m )=9.1 \times 10^{-31} kg$;
$1 eV =1.6 \times 10^{-19} J$ and
Planck's constant $( h )=6.6 \times 10^{-34} J - s$.
Energy of an electron $( E )=100 \times\left(1.6 \times 10^{-19}\right) J$
or $\lambda=\frac{h}{\sqrt{2 m E}}=\frac{6.6 \times 10^{-34}}{\sqrt{2 \times 9.1 \times 10^{-31} \times 100 \times 1.6 \times 10^{-19}}}$
$=1.2 \times 10^{-10} m =1.2 \,\mathring{A}$