question_answer 14)

The mass of an electron is \[9.1\times {{10}^{-31}}kg.\] If its K.E. is \[3\times {{10}^{-25}}J\], calculate its wavelength.

Answer:

Information shadow: Mass of electron \[(m)=9.1\times {{10}^{-31}}kg\] Kinetic energy of electron \[(E)=3\times {{10}^{-25}}J\] Planck's constant \['h'=6.626\times {{10}^{-34}}Js\] Problem solving strategy: If kinetic energy of the particle is given then its de Broglie wavelength can be calculated as: \[\lambda =\frac{h}{\sqrt{2Em}}\] Working it out: \[\lambda =\frac{6.626\times {{10}^{-34}}}{\sqrt{2\times 3\times {{10}^{-25}}\times 9.1\times {{10}^{-31}}}}\] \[=8.967\times {{10}^{-7}}m\] \[=8.96.7nm\].