Heisenberg’s Uncertainty Principle

It states that –It is impossible for small moving microscopic particle to calculate, both its position  and momentum simultaneously with absolute accuracy.

( either we can calculate its position or its momentum).

 

∆x.  ∆p   ≥   h/4л

∆x = uncertainty in position.

∆P= uncertainty in momentum.

∆x.  m∆V   >      h/4л

.∆x.  m∆V   = 5.27 x 10 -35

∆x = uncertainty in position.

∆V =uncertainty in velocity.

 

It may also be defined as the Product of uncertainty in position and uncertainty in momentum either equal to or greater than  h / 4л.

 

Accuracy of position depends upon the wavelength. Shorter the wavelength , greater the accuracy. But shorter the wavelength , higher the frequency and higher energy  which changes the speed of electron.

Shorter the wavelength , higher the momentum and hence greater uncertainty in velocity. On the other hand lower the momentum, higher the wavelength and hence greater the uncertainty in position.

 

Significance :  It has no significance in everyday life because everyday we come across the big objects , the position and velocity of which can be measured accurately.

 

The electron can not exists inside the nucleus because the diameter of atomic nucleus is 10-15 m . Mass of electron is

9.1 x 10-31 kg, the minimum uncertainty in velocity can be calculated by applying Heisenberg uncertainty principle.

 

∆x.  m∆V   =     h/4л

 

∆V    = 5.77 x 1010 m/s

 

This is the much higher value of velocity and can not exist inside the nucleus.

 

COMPTON EFFECT  - It may be defined as the phenomenon of increasing the wave length or decrease in frequency after scattering from the surface of lighter element

EXERCISE :

1.The uncertainty in the momentum of a particle is  2.2 x 10-4 Kg m s- . With what accuracy can its position  be determined .

a. 39 x 10-31 m.

b. 4 x 10-25 m

c. 2 x 10-20 m

d. none

  1. An e- has speed of 500 m/s with an uncertainty of 0.02%. What is the uncertainty on locating its position?                                                                                                                                  (a) 7 x 10-4                                                   (b) 6.77 x 10-6

(c) 3.75 x 10-10                                        (d) none

  1. Which of the following statements are wrong?

(a) Heisenberg's uncertainty principle is applicable only to microscopic         particles.

(b) de Broglie concept of dual nature is applicable to all material particles.

(c) The electronic configuration of palladium (Z = 46) is [Kr] 4d8

(d) dxy, dyz and dxz orbitals have identical shapes

  1. If the position of electron is measured with in an accuracy of 0.0002 nm, calculate the uncertainty in the momentum of electron.
  2. 2.638 x 10-23kgm/s b. 4.56 x 10-23kgm/s
  3. 0.342 x 10-23kgm/s   d.   6.78 x 10-23kgm/s
  4. The uncertainty in velocity of an electron if the uncertainty in position is 1 A0 or 100 pm (10-10 m) is
  5. 5.77 x 105 m/s b. 8.97 x 105 m/s
  6. 1.24 x 105 m/s d. 2.45 x 105 m/s

Answer 1. a 2. a 3. b, c 4. a 5. a

 

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