A golf ball has a mass of 40g and a speed of 45m/s. If the speed can be measured within accuracy of 2%, calculate the uncertainty in the position.

Solution

According to Heisenberg’s uncertainty principle,

space space space space space space space space space space increment straight x space space cross times space straight m increment straight v space equals space fraction numerator straight h over denominator 4 straight pi end fraction space space space space space space space or space space space increment straight x space equals space fraction numerator straight h over denominator 4 πm increment straight v end fraction space space space space space space space space space space space space... left parenthesis 1 right parenthesis space space space Here comma space space space space increment straight v space equals space fraction numerator 45 cross times 2 over denominator 100 end fraction space equals space 0.9 space ms to the power of negative 1 end exponent semicolon space space space space space space space space space space straight m space equals space 40 straight g space equals space 40 cross times 10 to the power of negative 3 end exponent kg space equals space 4 space cross times space 10 to the power of negative 2 end exponent kg space

Substituting the values in expression (1), we have,

space space space space increment straight x space equals space 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 4 space cross times 3.14 space cross times space left parenthesis 4 space cross times space 10 to the power of negative 2 end exponent kg right parenthesis space cross times space left parenthesis 0.9 space ms to the power of negative 1 end exponent right parenthesis end fraction space space space space space equals 1.46 space cross times 10 to the power of negative 33 end exponent straight m

Some More Questions From Structure of Atom Chapter

For Daily Free Study Material Join wiredfaculty