A microscope using suitable photons is employed to locate an electron in an atom within a distance of 0.1Å. What is the uncertainty involved in the measurement of its velocity?

Solution

According to Heisenberg’s uncertainty principle.

space space space space space space increment straight x space cross times space straight m increment straight v space greater or equal than space fraction numerator straight h over denominator 4 straight pi end fraction space space space or space space space space increment straight v space greater or equal than space fraction numerator straight h over denominator 4 straight pi cross times increment straight x cross times straight m end fraction space space space... left parenthesis 1 right parenthesis space space Here space straight m space equals space 9.11 space cross times space 10 to the power of negative 31 end exponent kg semicolon space space space space increment straight x space equals space 0.1 space straight Å space equals space 0.1 space cross times space 10 to the power of negative 10 end exponent straight m space space space space space straight h space equals space 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

Substituting the values in expression (1), we have

space space space space increment straight v 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 4 cross times 3.142 cross times left parenthesis 10 to the power of negative 10 end exponent straight m right parenthesis cross times left parenthesis 0.150 space kg right parenthesis end fraction space space space space space space equals space 3.52 space cross times space 10 to the power of negative 24 end exponent ms to the power of negative 1 end exponent

Some More Questions From Structure of Atom Chapter

For Daily Free Study Material Join wiredfaculty