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Structure Of Atom

Question
CBSEENCH11008438
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Given: The mass of electron is 9.11 x 10-31 kg
Planck constant is 6.626 x 10-34 Js,
the uncertainty involved in the measurement of velocity within a distance of 0.1 A is:

  • 5.79 x 106 ms-1

  • 5.79 x 107 ms-1

  • 5.79 x 108 ms-1

  • 5.79 x 105 ms-1

Solution

A.

5.79 x 106 ms-1

By Heisenberg's uncertainty principle
increment straight p space. increment straight x space greater or equal than space fraction numerator straight h over denominator 2 straight pi end fraction or space increment straight v. increment straight x space greater or equal than fraction numerator straight h over denominator 4 πm end fraction increment straight p space rightwards arrow space uncertainty space in space momentum increment straight x space rightwards arrow space uncertainty space in space position increment straight v space rightwards arrow space uncertainty space in space velocity straight m rightwards arrow space mass space of space particle Given comma increment straight x space equals space 0.1 space straight A space equals space 0.1 space straight x space 10 to the power of negative 10 end exponent space straight m straight m equals space 9.11 space straight x space 10 to the power of negative 31 end exponent space kg straight h space equals space planck space constant space equals space 6.626 space straight x space 10 to the power of negative 34 end exponent space Js straight pi space equals space 3.14 In space uncertain space position space increment straight v. increment straight x space equals space fraction numerator straight h over denominator 4 πm end fraction increment straight v space straight x space 0.1 space straight x space 10 to the power of negative 10 end exponent space equals space fraction numerator 6.626 space straight x space 10 to the power of negative 34 end exponent over denominator 4 space straight x space 3.14 space straight x space 9.11 space straight x space 10 to the power of negative 31 end exponent end fraction increment straight v space equals space fraction numerator 6.626 space straight x space 10 to the power of negative 34 end exponent over denominator 4 space straight x space 3.14 space straight x space 911 space straight x space 10 to the power of negative 31 end exponent straight x space 0.1 space straight x space 10 to the power of negative 1 end exponent end fraction ms to the power of negative 1 end exponent equals space 5.785 space straight x space 10 to the power of 6 space ms to the power of negative 1 end exponent 5.79 space straight x space 10 to the power of 6 space ms to the power of negative 1 end exponent

Some More Questions From Structure of Atom Chapter

Why were neutrons discovered very late?

What are the fundamental particles present in a neutral atom having atomic number greater than 1?

Do protons and neutrons have identical mass?

When α-particles are sent through a thin metal foil, most of them go straight through the foil. What inference do you draw from it?

What did Rutherford's experiment on scattering of particles show for the first time?

What is Plum-Pudding model of the atom?

Are neutrons present in all atoms?

Why are electrons called planetary electrons?

What are nucleons?

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