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Structure Of Atom

Question
CBSEENCH11005305

Similar to electron diffraction, neutron diffraction microscope is also used for the determination of the structure of molecules. If the wavelength used here is 800 pm, calculate the characteristic velocity associated with the neutron.

Solution
According to de-Broglie equation.
      space space space space space space space straight lambda space equals space straight h over mv space space or space space straight v space equals space fraction numerator straight h over denominator straight m space cross times space straight lambda end fraction space space space space space... left parenthesis 1 right parenthesis
Here space straight h space equals space 6.626 space cross times 10 to the power of negative 34 end exponent space kg space straight m squared straight s to the power of negative 1 end exponent semicolon
Mass space of space neutron space left parenthesis straight m right parenthesis space equals space 1.675 space cross times 10 to the power of negative 27 end exponent kg semicolon
space space space space space space space space space space space space space space space space space space space space space space space space straight v space equals space 800 space cross times space 10 to the power of negative 12 end exponent straight m
Substituting space the space values space in space left parenthesis 1 right parenthesis comma space we space have
straight v space equals fraction numerator 6.626 space cross times space 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 1.675 space cross times 10 to the power of negative 27 end exponent kg space cross times left parenthesis 800 space cross times 10 to the power of negative 12 end exponent straight m right parenthesis end fraction
space space space equals 4.94 space cross times space 10 to the power of 4 space ms to the power of negative 1 end exponent