Dual behaviour of matter proposed by de Broglie led to the discovery of electron microscope often used for the highly magnified images of biological molecules and other type of material. If the velocity of the leectron in this microscope is 1.6 X 10⁶ ms^-1, calculate de Broglie wavelength associated with this electron.

Solution

According to de-Broglie equation,

space space space straight lambda space equals straight h over mv

...(1)

Here space straight h space equals space 6.626 space cross times 10 to the power of negative 34 end exponent kg space straight m squared straight s to the power of negative 1 end exponent straight m space equals 9.11 space cross times 10 to the power of negative 31 end exponent kg semicolon space space space straight v space equals space 1.6 cross times 10 to the power of 6 space ms to the power of negative 1 end exponent

Substituting the values in equation (1), we have

space space space space space space straight lambda space equals space fraction numerator 6.626 space cross times 10 to the power of negative 34 end exponent kg space straight m squared straight s to the power of negative 1 end exponent over denominator left parenthesis 9.11 space cross times space 10 to the power of negative 31 end exponent space kg right parenthesis space cross times space left parenthesis 1.6 space cross times 10 to the power of 6 space ms to the power of negative 1 end exponent right parenthesis end fraction space space space space space space space space equals space 4.55 space cross times 10 to the power of negative 10 end exponent straight m space equals space 455 space pm

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