Question

If an electron has an energy such that its de-Broglie wavelength is $5500\,\mathring{A}$, then the energy value of that electron is
$\left(h=6.6 \times 10^{-34} Js , m_{ C }=9.1 \times 10^{-31} kg \right)$

• A. $8 \times 10^{-20} J$
• B. $8 \times 10^{-10} J$
• C. $8 J$
• D. $8 \times 10^{-25} J$

Answer 1

Answer: (D)

de-Broglie wavelength
$\lambda =\frac{h}{\sqrt{2\, m E}}$
$E =\frac{1}{2 \,m}\left(\frac{h}{\lambda}\right)^{2} $
$=\frac{1}{2 \times 9.1 \times 10^{-31}}\left(\frac{6.625 \times 10^{-34}}{5.5 \times 10^{-7}}\right)^{2} $
$=\frac{1}{18.2 \times 10^{-31}} \times 1.45 \times 10^{-54} $
$=8 \times 10^{-25} \,J$