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Q.45 - Excercises And Problems

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 1118

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Short Answer

Soot particles, from incomplete combustion in diesel engines, are typically in diameter and have a density of . FIGURE P39.45 shows soot particles released from rest, in vacuum, just above a thin plate with a -diameter holeroughly the wavelength of visible light. After passing through the hole, the particles fall distance and land on a detector. If soot particles were purely classical, they would fall straight down and, ideally, all land in a -diameter circle. Allowing for some experimental imperfections, any quantum effects would be noticeable if the circle diameter were . How far would the particles have to fall to fill a circle of this diameter?

Hence, the particle would have to fall to fill a circle of diameter of

See the step by step solution

Step by Step Solution

 Step 1: Given Informaiton

Soot particles diameter


Diameter of thin plate

Diameter of the circle=2000 nm

 Step 2: solution

Formula to be used:

The uncertainity principle is given by

Where, is measurement of position, is measurement of the momentum of the particle and is planks constant.


The mass of the particle is given by

[considering the shape of particle is sphere]

Where is mass, is density and is diameter

Applying values,

The minimum uncertainity momentum is given by,

Applying values,

The momentum and energy relation is given by

[where is measurement of energy of particle]

Applying values,

The potential energy of the falling particle is given by,

Where v is height of potential barrier, m is mass, g is acceleration due to gravity and d is distance of falling particle.

The relation between potential energy and uncertainty energy is given by [P.E of particle should be more or equal to ]

Applying values,

Conclusion:Hence, the particle would have to fall to fill a circle of diameter of .

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