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Q.45 - Excercises And Problems

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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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

Density=

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.

Calculation:

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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