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QUESTIONS on Heisenberg uncertainty principle


QUESTIONS on Heisenberg uncertainty principle 1

Determine the Heisenberg uncertainty in the

  1. Energy of photon which is radiated in time interval of 10-5s
  2. Momentum of 0.2kg football moving with a speed of 20ms-1 and restricted to a region of 25cm
  3. Determine the fractional  uncertainty in momentum too.

Solution

(1) using

\triangle E\triangle t\quad \ge \frac { h }{ 2\pi } ,\quad that\quad is\quad \triangle E\quad \ge \quad \frac { 6.63\quad \times \quad { 10 }^{ -34 } }{ 2\times \pi \times { 10 }^{ -29 } } \quad \ge \quad 1.06\times { 10 }^{ -29 }J

 

(2) using

\triangle p\triangle x\quad \ge \frac { h }{ 2\pi } \quad =\frac { 6.63\times { 10 }^{ -34 } }{ 2\pi } \quad =4.2\times { 10 }^{ -34 }

 

(3) Using

\frac { \triangle { p }_{ x } }{ { p }_{ x } } \quad =\frac { 4.2\times { 10 }^{ -34 } }{ 4 } \quad =\quad 1.05\quad \times \quad { 10 }^{ -34 }

 

QUESTIONS on Heisenberg uncertainty principle 2

(4)  The Heisenberg uncertainty principle can be wrtten as

I) \triangle p\triangle x\quad >\frac { h }{ 2\pi } 

II) \triangle xh\quad \ge \quad \frac { \triangle p }{ 2\pi }

III) \triangle E\triangle t\ge \frac { h }{ 2\pi }

 

ANSWERS are I and III

QUESTIONS on Heisenberg uncertainty principle 5

 

A 0.01kg of football moving with a speed of 20ms-1 is restricted to a region of 20cm. calculate:

I) the uncertainty in momentum

II) the fractional uncertainty in momentum

Solution

I) using

\triangle x\triangle p=\frac { h }{ 2\pi } ,\quad that\quad is\quad \triangle p=\frac { h }{ 2\pi \triangle x } =\frac { 6.63\times { 10 }^{ -34 } }{ 2\times 3.142\times 0.2 } =5.3\times { 10 }^{ -34 }

 

II) using

\frac { \triangle p }{ { p }_{ x } } =\frac { 5.3\times { 10 }^{ -34 } }{ 0.10\times 25 }              =2.1\times { 10 }^{ -34 }

To understand Heisenberg uncertainty principle read it here

 

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