# 5.8 The particle-wave duality reviewed  (Page 2/3)

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## Problem-solving strategy

1. Identify which physical principles are involved.
2. Solve the problem using strategies outlined in the text.

[link] illustrates how these strategies are applied to an integrated-concept problem.

## Recoil of a dust particle after absorbing a photon

The following topics are involved in this integrated concepts worked example:

 Photons (quantum mechanics) Linear Momentum

A 550-nm photon (visible light) is absorbed by a $1\text{.}\text{00-μg}$ particle of dust in outer space. (a) Find the momentum of such a photon. (b) What is the recoil velocity of the particle of dust, assuming it is initially at rest?

Strategy Step 1

To solve an integrated-concept problem , such as those following this example, we must first identify the physical principles involved and identify the chapters in which they are found. Part (a) of this example asks for the momentum of a photon , a topic of the present chapter. Part (b) considers recoil following a collision , a topic of Linear Momentum and Collisions .

Strategy Step 2

The following solutions to each part of the example illustrate how specific problem-solving strategies are applied. These involve identifying knowns and unknowns, checking to see if the answer is reasonable, and so on.

Solution for (a)

The momentum of a photon is related to its wavelength by the equation:

$p=\frac{h}{\lambda }.$

Entering the known value for Planck’s constant $h$ and given the wavelength $\lambda$ , we obtain

$\begin{array}{lll}p& =& \frac{\text{6.63}×{\text{10}}^{-\text{34}}\phantom{\rule{0.25em}{0ex}}\text{J}\cdot s}{\text{550}×{\text{10}}^{–9}\phantom{\rule{0.25em}{0ex}}\text{m}}\\ & =& 1\text{.}\text{21}×{\text{10}}^{-\text{27}}\phantom{\rule{0.25em}{0ex}}\text{kg}\cdot \text{m/s}\text{.}\end{array}$

Discussion for (a)

This momentum is small, as expected from discussions in the text and the fact that photons of visible light carry small amounts of energy and momentum compared with those carried by macroscopic objects.

Solution for (b)

Conservation of momentum in the absorption of this photon by a grain of dust can be analyzed using the equation:

${p}_{1}+{p}_{2}={p\prime }_{1}+{p\prime }_{2}\left({F}_{\text{net}}=0\right).$

The net external force is zero, since the dust is in outer space. Let 1 represent the photon and 2 the dust particle. Before the collision, the dust is at rest (relative to some observer); after the collision, there is no photon (it is absorbed). So conservation of momentum can be written

${p}_{1}={p\prime }_{2}=\text{mv},$

where ${p}_{1}$ is the photon momentum before the collision and ${p\prime }_{2}$ is the dust momentum after the collision. The mass and recoil velocity of the dust are $m$ and $v$ , respectively. Solving this for $v$ , the requested quantity, yields

$v=\frac{p}{m},$

where $p$ is the photon momentum found in part (a). Entering known values (noting that a microgram is ${\text{10}}^{-9}\phantom{\rule{0.25em}{0ex}}\text{kg}$ ) gives

$\begin{array}{lll}v& =& \frac{1\text{.}\text{21}×{\text{10}}^{-\text{27}}\phantom{\rule{0.25em}{0ex}}\text{kg}\cdot \text{m/s}}{1\text{.}\text{00}×{\text{10}}^{–9}\phantom{\rule{0.25em}{0ex}}\text{kg}}\\ & =& 1\text{.}\text{21}×{\text{10}}^{\text{–18}}\phantom{\rule{0.25em}{0ex}}\text{m/s.}\end{array}$

Discussion

The recoil velocity of the particle of dust is extremely small. As we have noted, however, there are immense numbers of photons in sunlight and other macroscopic sources. In time, collisions and absorption of many photons could cause a significant recoil of the dust, as observed in comet tails.

## Section summary

• The particle-wave duality refers to the fact that all particles—those with mass and those without mass—have wave characteristics.
• This is a further connection between mass and energy.

## Conceptual questions

In what ways are matter and energy related that were not known before the development of relativity and quantum mechanics?

#### Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
how did you get the value of 2000N.What calculations are needed to arrive at it
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