# 29.8 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?

example ofchange of state of the body in the effectof heat
what is normal force?
the force that pushes upward on us. the force that opposes gravity
clifford
upthrust of air
Newton's 3rd law. the force of the ground (earth) that pushes back on gravity, keeping us on the ground instead of sinking into it.
clifford
I really need lots of questions on frictional force
Shii
I can help answering what I can
Shii
does friction also need some force to perform?
Mohit
no friction is a force just like the gravitational force
clifford
yeah but u can't apply friction anywhere else like other forces
Mohit
I don't understand that question. friction does work alongside other forces based on the situation.
clifford
eg. when walking there are two forces acting on us gravitational and frictional force. friction helps us move forward and gravity keeps us on the ground
clifford
friction is a contact force. Two surfaces are necessary for the force to work.
clifford
hope this helped
clifford
the friction force which oppose while it contact with surrounding. there are two kind of friction. slidding and rolling friction.
Neyaz
Two unequal masses M1 and M2 are connected by a string of tension T on a plane,find the acceleration and tension in the string
Ogboru
derive the equation
Ogboru
What is physics?
physics is a branch of science in which we are dealing with the knowledge of our physical things. macroscopic as well as microscopic. we are going look inside the univers with the help of physics. you can learn nature with the help of physics. so many branches of physics you have to learn physics.
vijay
What are quarks?
6 type of quarks
Neyaz
what is candela
Candela is the unit for the measurement of light intensity.
Osei
any one can prove that 1hrpower= 746 watt
Newton second is the unit of ...............?
Neyaz
Impulse and momentum
Fauzia
force×time and mass× velocity
vijay
Good
Neyaz
What is the simple harmonic motion?
oscillatory motion under a retarding force proportional to the amount of displacement from an equilibrium position
Yuri
Straight out of google, you could do that to, I suppose.
Yuri
*too
Yuri
ok
Fauzia
Oscillatory motion under a regarding force proportional to the amount of displacement from an equilibrium position
Neyaz
examples of work done by load of gravity
What is ehrenfest theorem?
You can look it up, faster and more reliable answer.
Yuri
That isn't a question to ask on a forum and I also have no idea what that is.
Yuri
what is the work done by gravity on the load 87kj,11.684m,mass xkg[g=19m/s
Maureen
What is law of mass action?
rate of chemical reactions is proportional to concentration of reactants ...
ok thanks
Fauzia
what is lenses
lenses are two types
Fauzia
concave and convex
right
Fauzia
speed of light in space
in vacuum speed of light is 3×10^8 m/s
vijay
ok
Vikash
2.99×10^8m/s
Umair
2.8820^8m/s
Muhammed
Vikash
he is correct but we can round up in simple terms
vijay
3×10^8m/s
vijay
is it correct
Fauzia
I mean 3*10^8 m/s ok
vijay
299792458 meter per second
babar
3*10^8m/s
Neyaz
how many Maxwell relations in thermodynamics
vijay
how we can do prove them?
vijay
What is second law of thermodynamics?
Neyaz
please who has a detailed solution to the first two professional application questions under conservation of momentum
I want to know more about pressure
Osei
I can help
Emeh
okay go on
True
I mean on pressure
Emeh
definition of Pressure
John
it is the force per unit area of a substance.S.I unit is Pascal 1pascal is defined as 1N acting on 1m² area i.e 1pa=1N/m²
Emeh
pls explain Doppler effect
Emmex
solve this an inverted differential manometer containing oil specific gravity 0.9 and manometer reading is 400mm find the difference of pressure