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

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## Problems&Exercises

Integrated Concepts

The 54.0-eV electron in [link] has a 0.167-nm wavelength. If such electrons are passed through a double slit and have their first maximum at an angle of $\text{25}\text{.}0º$ , what is the slit separation $d$ ?

0.395 nm

Integrated Concepts

An electron microscope produces electrons with a 2.00-pm wavelength. If these are passed through a 1.00-nm single slit, at what angle will the first diffraction minimum be found?

Integrated Concepts

A certain heat lamp emits 200 W of mostly IR radiation averaging 1500 nm in wavelength. (a) What is the average photon energy in joules? (b) How many of these photons are required to increase the temperature of a person’s shoulder by $2\text{.}0º\text{C}$ , assuming the affected mass is 4.0 kg with a specific heat of $0\text{.83 kcal}\text{/kg}\cdot \text{ºC}$ . Also assume no other significant heat transfer. (c) How long does this take?

(a) $1.3×{\text{10}}^{-\text{19}}\phantom{\rule{0.25em}{0ex}}\text{J}$

(b) $2\text{.}1×{\text{10}}^{\text{23}}$

(c) $1\text{.}4×{\text{10}}^{2}\phantom{\rule{0.25em}{0ex}}\text{s}$

Integrated Concepts

On its high power setting, a microwave oven produces 900 W of 2560 MHz microwaves. (a) How many photons per second is this? (b) How many photons are required to increase the temperature of a 0.500-kg mass of pasta by $\text{45}\text{.}0º\text{C}$ , assuming a specific heat of $0\text{.}\text{900 kcal/kg}\cdot \text{ºC}$ ? Neglect all other heat transfer. (c) How long must the microwave operator wait for their pasta to be ready?

Integrated Concepts

(a) Calculate the amount of microwave energy in joules needed to raise the temperature of 1.00 kg of soup from $\text{20}\text{.}0º\text{C}$ to $\text{100}\text{ºC}$ . (b) What is the total momentum of all the microwave photons it takes to do this? (c) Calculate the velocity of a 1.00-kg mass with the same momentum. (d) What is the kinetic energy of this mass?

(a) $3\text{.}\text{35}×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{J}$

(b) $1\text{.}\text{12}×{\text{10}}^{\text{–3}}\phantom{\rule{0.25em}{0ex}}\text{kg}\cdot \text{m/s}$

(c) $1\text{.}\text{12}×{\text{10}}^{\text{–3}}\phantom{\rule{0.25em}{0ex}}\text{m/s}$

(d) $6.23×{\text{10}}^{\text{–7}}\phantom{\rule{0.25em}{0ex}}\text{J}$

Integrated Concepts

(a) What is $\gamma$ for an electron emerging from the Stanford Linear Accelerator with a total energy of 50.0 GeV? (b) Find its momentum. (c) What is the electron’s wavelength?

Integrated Concepts

(a) What is $\gamma$ for a proton having an energy of 1.00 TeV, produced by the Fermilab accelerator? (b) Find its momentum. (c) What is the proton’s wavelength?

(a) $1\text{.}\text{06}×{\text{10}}^{3}$

(b) $5\text{.}\text{33}×{\text{10}}^{-\text{16}}\phantom{\rule{0.25em}{0ex}}\text{kg}\cdot \text{m/s}$

(c) $1\text{.}\text{24}×{\text{10}}^{-\text{18}}\phantom{\rule{0.25em}{0ex}}\text{m}$

Integrated Concepts

An electron microscope passes 1.00-pm-wavelength electrons through a circular aperture $2\text{.}\text{00 μm}$ in diameter. What is the angle between two just-resolvable point sources for this microscope?

Integrated Concepts

(a) Calculate the velocity of electrons that form the same pattern as 450-nm light when passed through a double slit. (b) Calculate the kinetic energy of each and compare them. (c) Would either be easier to generate than the other? Explain.

(a) $1\text{.}\text{62}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m/s}$

(b) $4\text{.}\text{42}×{\text{10}}^{-\text{19}}\phantom{\rule{0.25em}{0ex}}\text{J}$ for photon, $1\text{.}\text{19}×{\text{10}}^{-\text{24}}\phantom{\rule{0.25em}{0ex}}\text{J}$ for electron, photon energy is $3\text{.}\text{71}×{\text{10}}^{5}$ times greater

(c) The light is easier to make because 450-nm light is blue light and therefore easy to make. Creating electrons with $7.43 \mu eV$ of energy would not be difficult, but would require a vacuum.

Integrated Concepts

(a) What is the separation between double slits that produces a second-order minimum at $\text{45}\text{.}0º$ for 650-nm light? (b) What slit separation is needed to produce the same pattern for 1.00-keV protons.

(a) $2\text{.}\text{30}×{\text{10}}^{-6}\phantom{\rule{0.25em}{0ex}}\text{m}$

(b) $3\text{.}\text{20}×{\text{10}}^{-\text{12}}\phantom{\rule{0.25em}{0ex}}\text{m}$

Integrated Concepts

A laser with a power output of 2.00 mW at a wavelength of 400 nm is projected onto calcium metal. (a) How many electrons per second are ejected? (b) What power is carried away by the electrons, given that the binding energy is 2.71 eV? (c) Calculate the current of ejected electrons. (d) If the photoelectric material is electrically insulated and acts like a 2.00-pF capacitor, how long will current flow before the capacitor voltage stops it?

Integrated Concepts

One problem with x rays is that they are not sensed. Calculate the temperature increase of a researcher exposed in a few seconds to a nearly fatal accidental dose of x rays under the following conditions. The energy of the x-ray photons is 200 keV, and $4\text{.}\text{00}×{\text{10}}^{\text{13}}$ of them are absorbed per kilogram of tissue, the specific heat of which is $0\text{.}\text{830 kcal/kg}\cdot \text{ºC}$ . (Note that medical diagnostic x-ray machines cannot produce an intensity this great.)

$3\text{.}\text{69}×{\text{10}}^{-4}\phantom{\rule{0.25em}{0ex}}\mathrm{ºC}$

Integrated Concepts

A 1.00-fm photon has a wavelength short enough to detect some information about nuclei. (a) What is the photon momentum? (b) What is its energy in joules and MeV? (c) What is the (relativistic) velocity of an electron with the same momentum? (d) Calculate the electron’s kinetic energy.

Integrated Concepts

The momentum of light is exactly reversed when reflected straight back from a mirror, assuming negligible recoil of the mirror. Thus the change in momentum is twice the photon momentum. Suppose light of intensity $1\text{.}{\text{00 kW/m}}^{2}$ reflects from a mirror of area $2\text{.}{\text{00 m}}^{2}$ . (a) Calculate the energy reflected in 1.00 s. (b) What is the momentum imparted to the mirror? (c) Using the most general form of Newton’s second law, what is the force on the mirror? (d) Does the assumption of no mirror recoil seem reasonable?

(a) 2.00 kJ

(b) $1\text{.}\text{33}×{\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}\text{kg}\cdot \text{m/s}$

(c) $1\text{.}\text{33}×{\text{10}}^{-5}\phantom{\rule{0.25em}{0ex}}\text{N}$

(d) yes

Integrated Concepts

Sunlight above the Earth’s atmosphere has an intensity of $1\text{.}\text{30}\phantom{\rule{0.25em}{0ex}}{\text{kW/m}}^{2}$ . If this is reflected straight back from a mirror that has only a small recoil, the light’s momentum is exactly reversed, giving the mirror twice the incident momentum. (a) Calculate the force per square meter of mirror. (b) Very low mass mirrors can be constructed in the near weightlessness of space, and attached to a spaceship to sail it. Once done, the average mass per square meter of the spaceship is 0.100 kg. Find the acceleration of the spaceship if all other forces are balanced. (c) How fast is it moving 24 hours later?

#### Questions & Answers

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
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
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