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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 25 . size 12{"25" "." 0°} {} , what is the slit separation d size 12{d} {} ?

0.395 nm

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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?

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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 . C size 12{2 "." 0°C} {} , assuming the affected mass is 4.0 kg with a specific heat of 0 .83 kcal /kg ºC size 12{0 "." "83"" kcal/kg" cdot °C} {} . Also assume no other significant heat transfer. (c) How long does this take?

(a) 1.3 × 10 19 J size 12{1 "." "33" times "10" rSup { size 8{ - "19"} } " J"} {}

(b) 2 . 1 × 10 23 size 12{2 "." 1 times "10" rSup { size 8{"23"} } } {}

(c) 1 . 4 × 10 2 s size 12{1 "." 4 times "10" rSup { size 8{2} } " s"} {}

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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 45 . C size 12{"45" "." 0°C} {} , assuming a specific heat of 0 . 900 kcal/kg ºC size 12{0 "." "900"" kcal/kg" cdot °C} {} ? Neglect all other heat transfer. (c) How long must the microwave operator wait for their pasta to be ready?

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Integrated Concepts

(a) Calculate the amount of microwave energy in joules needed to raise the temperature of 1.00 kg of soup from 20 . C size 12{"20" "." 0°C} {} to 100 ºC size 12{"100"°C} {} . (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 . 35 × 10 5 J size 12{3 "." "35" times "10" rSup { size 8{5} } " J"} {}

(b) 1 . 12 × 10 –3 kg m/s size 12{1 "." "12" times "10" rSup { size 8{"–3"} } " kg" cdot "m/s"} {}

(c) 1 . 12 × 10 –3 m/s size 12{1 "." "12" times "10" rSup { size 8{"–3"} } " m/s"} {}

(d) 6.23 × 10 –7 J size 12{6 "." "23" times "10" rSup { size 8{"–7"} } " J"} {}

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Integrated Concepts

(a) What is γ size 12{γ} {} 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?

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Integrated Concepts

(a) What is γ size 12{γ} {} 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 . 06 × 10 3 size 12{1 "." "07" times "10" rSup { size 8{3} } } {}

(b) 5 . 33 × 10 16 kg m/s size 12{5 "." "34" times "10" rSup { size 8{ - "16"} } `"kg" cdot "m/s"} {}

(c) 1 . 24 × 10 18 m size 12{1 "." "24" times "10" rSup { size 8{ - "18"} } `m} {}

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Integrated Concepts

An electron microscope passes 1.00-pm-wavelength electrons through a circular aperture 2 . 00 μm size 12{2 "." "00 μm"} {} in diameter. What is the angle between two just-resolvable point sources for this microscope?

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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 . 62 × 10 3 m/s size 12{1 "." "62" times "10" rSup { size 8{3} } " m/s"} {}

(b) 4 . 42 × 10 19 J size 12{4 "." "41" times "10" rSup { size 8{ - "19"} } " J"} {} for photon, 1 . 19 × 10 24 J size 12{1 "." "19" times "10" rSup { size 8{ - "24"} } `J} {} for electron, photon energy is 3 . 71 × 10 5 size 12{3 "." "71" times "10" rSup { size 8{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 μeV size 12{7 "." "43"`"μeV"} {} of energy would not be difficult, but would require a vacuum.

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Integrated Concepts

(a) What is the separation between double slits that produces a second-order minimum at 45 . size 12{"45" "." 0°} {} for 650-nm light? (b) What slit separation is needed to produce the same pattern for 1.00-keV protons.

(a) 2 . 30 × 10 6 m size 12{2 "." "30" times "10" rSup { size 8{ - 6} } " m"} {}

(b) 3 . 20 × 10 12 m size 12{3 "." "20" times "10" rSup { size 8{ - "12"} } `m} {}

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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?

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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 . 00 × 10 13 size 12{4 "." "00" times "10" rSup { size 8{"13"} } } {} of them are absorbed per kilogram of tissue, the specific heat of which is 0 . 830 kcal/kg ºC size 12{0 "." "830"" kcal/kg" cdot °C} {} . (Note that medical diagnostic x-ray machines cannot produce an intensity this great.)

3 . 69 × 10 4 ºC size 12{3 "." "69" times "10" rSup { size 8{ - 4} } `°C} {}

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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.

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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 . 00 kW/m 2 size 12{1 "." "00 kW/m" rSup { size 8{2} } } {} reflects from a mirror of area 2 . 00 m 2 size 12{2 "." "00 m" rSup { size 8{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 . 33 × 10 5 kg m/s size 12{1 "." "33" times "10" rSup { size 8{ - 5} } `"kg" cdot "m/s"} {}

(c) 1 . 33 × 10 5 N size 12{1 "." "33" times "10" rSup { size 8{ - 5} } " N"} {}

(d) yes

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Integrated Concepts

Sunlight above the Earth’s atmosphere has an intensity of 1 . 30 kW/m 2 size 12{1 "." "30"" kW/m" rSup { size 8{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?

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Questions & Answers

Why is the sky blue...?
Star Reply
It's filtered light from the 2 forms of radiation emitted from the sun. It's mainly filtered UV rays. There's a theory titled Scatter Theory that covers this topic
Mike
A heating coil of resistance 30π is connected to a 240v supply for 5min to boil a quantity of water in a vessel of heat capacity 200jk. If the initial temperature of water is 20°c and it specific heat capacity is 4200jkgk calculate the mass of water in a vessel
fasawe Reply
A thin equi convex lens is placed on a horizontal plane mirror and a pin held 20 cm vertically above the lens concise in position with its own image the space between the undersurface of d lens and the mirror is filled with water (refractive index =1•33)and then to concise with d image d pin has to
Azummiri Reply
Be raised until its distance from d lens is 27cm find d radius of curvature
Azummiri
what happens when a nuclear bomb and atom bomb bomb explode add the same time near each other
FlAsH Reply
A monkey throws a coconut straight upwards from a coconut tree with a velocity of 10 ms-1. The coconut tree is 30 m high. Calculate the maximum height of the coconut from the top of the coconut tree? Can someone answer my question
Fatinizzah Reply
v2 =u2 - 2gh 02 =10x10 - 2x9.8xh h = 100 ÷ 19.6 answer = 30 - h.
Ramonyai
why is the north side is always referring to n side of magnetic
sam Reply
who is a nurse
Chilekwa Reply
A nurse is a person who takes care of the sick
Bukola
a nurse is also like an assistant to the doctor
Gadjawa
explain me wheatstone bridge
Malik Reply
good app
samuel
Wheatstone bridge is an instrument used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component.
MUHD
Rockwell Software is Rockwell Automation’s "Retro Encabulator". Now, basically the only new principle involved is that instead of power being generated by the relative motion of conductors and fluxes, it’s produced by the modial interaction of magneto-reluctance and capacitive diractance. The origin
Chip
what refractive index
Adjah Reply
write a comprehensive note on primary colours
Harrison Reply
relationship between refractive index, angle of minimum deviation and angle of prism
Harrison
Who knows the formula for binding energy,and what each variable or notation stands for?
Agina Reply
1. A black thermocouple measures the temperature in the chamber with black walls.if the air around the thermocouple is 200 C,the walls are at 1000 C,and the heat transfer constant is 15.compute the temperature gradient
Tikiso Reply
what is the relationship between G and g
Olaiya Reply
G is the u. constant, as g stands for grav, accelerate at a discreet point
Mark
Is that all about it?
Olaiya
pls explain in details
Olaiya
G is a universal constant
Mark
g stands for the gravitational acceleration point. hope this helps you.
Mark
balloon TD is at a gravitational acceleration at a specific point
Mark
I'm sorry this doesn't take dictation very well.
Mark
Can anyone explain the Hooke's law of elasticity?
Olaiya Reply
extension of a spring is proportional to the force applied so long as the force applied does not exceed the springs capacity according to my textbook
Amber
does this help?
Amber
Yes, thanks
Olaiya
so any solid can be compressed how compressed is dependent upon how much force is applied F=deltaL
Amber
sorry, the equation is F=KdeltaL delta is the triangle symbol and L is length so the change in length is proportional to amount of Force applied I believe that is what Hookes law means. anyone catch any mistakes here please correct me :)
Amber
I think it is used only for solids and not liquids, isn't it?
Olaiya
basically as long as you dont exceed the elastic limit the object should return to it original form but if you exceed this limit the object will not return to original shape as it will break
Amber
Thanks for the explanation
Olaiya
yh, liquids don't apply here, that should be viscosity
Chiamaka
hope it helps 😅
Amber
also, an object doesnt have to break necessarily, but it will have a new form :)
Amber
Yes
Olaiya
yeah, I think it is for solids but maybe there is a variation for liquids? that I am not sure of
Amber
ok
Olaiya
good luck!
Amber
Same
Olaiya
aplease i need a help on spcific latent heat of vibrations
Bilgate
specific latent heat of vaporisation
Bilgate
how many kilometers makes a mile
Margaret Reply
about 1.6 kilometres.
Faizyab
near about 1.67 kilometers
Aakash
equal to 1.609344 kilometers.
MUHD

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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