Question

The kinetic energy of an electron is $9.1\times {10}^{-25}J$. Calculate the de Broglie wavelength for the same.
$(\text{Planck's constant},h=6.6\times {10}^{-34}Js,\text{mass of electron}=9.1\times {10}^{-31}kg)$

• A. $0.51\times {10}^{-5}m$
• B. $0.51\times {10}^{-6}m$
• C. $0.51\times {10}^{-7}m$
• D. $0.51\times {10}^{-8}m$

Answer 1

The correct option is B $0.51\times {10}^{-6}m$

Given:
$\text{Kinetic energy}(K.E.)=9.1\times {10}^{-25}J$
$\text{Mass of electron}\left(m_e\right)=9.1\times {10}^{-31}kg\text{Planck's constant}\left(h\right)=6.6\times {10}^{-34}Js$

We know,
$\text{de Broglie wavelength}\left(\lambda \right)=\frac{h}{\sqrt{2K.E.m_e}}=\frac{6.6\times {10}^{-34}J-sec}{\sqrt{2\times 9.1\times {10}^{-25}\times 9.1\times {10}^{-31}}}=0.51\times {10}^{-6}m$