Practice: What is the speed of an electron that has a wavelength of 895 μm? (Mass of an electron = 9.11 x 10^{ -31} kg)

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The **De Broglie Wavelength** equation relates wavelength to velocity or speed.

Concept #1: The De Broglie Wavelength Equation

**Transcript**

In this new video, we're going to take a look at the wave nature of light. Now, we've talked about light being composed of small packets of electromagnetic energy. We say that each one of these packets of this energy were called quantums way long ago. In modern days now, we call them photons, so we say light is composed of small particles called photons, but we've also talked about the inverse relationships of frequency and wavelength. In those examples, we've talked about light moving as a wave.

In this section, we're going to stick to that type of idea. We're going to see light as moving not as individualized particles but rather as a wave. We're going to say there's an equation that shares this relationship of light moving as a wave. It's called de Broglie wavelength equation. Under this equation, it says light moves as a wave, not as individual photons, individual particles. Now, we're going to say to calculate the wavelength of matter, we simply use this equation.

Now, the equation is for de Broglie wavelength equation is, lambda which is our wavelength equals h which is Planck's constant divided by m times v. We know that lambda is wavelength in meters. H is Planck's constant which we've talked about. Here m represents the mass of the object we're talking about. Usually, this object is subatomic particle. Here it will be the mass in kilograms, not in grams. v does not represent our frequency anymore. V here is actually velocity or speed. Velocity or speed are in meters per second.

What we need to realize here about Planck's constant is Planck's constant is 6.626 x 10-34 joules times seconds. We should realize that joules can be written a different way. Joules also equal kilograms times meters squared over seconds squared. That's what joules equal. If our joules are still multiplying with those seconds, then seconds will be canceled out with one of the seconds here.

In this equation, we're going to say Planck's constant becomes 6.626 x 10-34 kilograms times meters squared over seconds. Just realize how those things canceled out to give me that. Those are the units that you're going to have to remember when it deals with de Broglie wavelength.

Example #1: Find the wavelength (in nm) of a proton with a speed of 7.33 x 10** ^{9}** . (Mass of a proton = 1.67 x 10

Practice: What is the speed of an electron that has a wavelength of 895 μm? (Mass of an electron = 9.11 x 10^{ -31} kg)

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Calculate the wavelength in meters for a bullet weighing 5.0 g and traveling at 400 m/sec.
A) 3.3 x 10-34 m
B) 5.8 x 10-19 m
C) 1.5 x 10-38 m
D) 3.0 x 1033 m
E) 3.3 x 10-37 m

Calculate the DeBroglie wavelength of an electron traveling with a velocity of 4.0 x 10 9 cm/sec in an electron microscope.
A. 0.18 Å
B. 67 Å
C. 1.5 Å
D. 0.0018 Å
E. 1.1 x 10-38 Å

In a scanning electron microscope (SEM), electrons are accelerated to great velocities. Calculate the wavelength of an electron traveling with a velocity of 1.7 x 104 meters per second. The mass of an electron is 9.1 x 10-28 g?
a) 4.3 x 10 -11 m
b) 4.3 x 10 -8 m
c) 1.8 x 10 4 m
d) 2.3 x 10 -35 m
e) 2 x 10 -33 m

Calculate the wavelength in nanometers for a bullet weighing 5.0 g and traveling at 400 m/sec.
A) 3.3 x 10-34 m
B) 5.8 x 10-19 m
C) 1.5 x 10-38 m
D) 3.0 x 1033 m
E) 3.3 x 10-37 m

The de Broglie wavelength for a baseball moving at 25.0 m/s is 2 x 10-34 m. If a baseball could travel at the speed of light, what would be its de Broglie wavelength at that speed?
A) 1.7 x 10-41 m
B) 1.5 x 10-26 m
C) 1.7 x 10-43 m
D) 1.5 x 10-28 m
E) 1.5 x 10-24 m

What is the de Broglie wavelength of a bird being chased by Schrodinger’s cat, Albert? The bird has a mass of 0.5 kg and is flying at 20 m/s.
1. 6.626 × 10−35 m
2. 6.626 × 103 m
3. 6.626 × 10−38 m
4. 6.626 × 10−18 m
5. 6.626 × 10−15 m

Neutron diffraction is an important technique for determining the structures of molecules.Calculate the velocity of a neutron needed to achieve a wavelength of 1.35 Å . (Take the mass of the neutron m=1.674910-27kg).

The deBroglie wavelength can become significant for an object that is:A. low in mass and low in velocityB. low in mass and high in velocityC. high in mass and low in velocityD. high in mass and high in velocityE. found in degenerate orbitals

An electron (mass = 9.11x10 -31 kg) moves with a velocity of 5.00x10 8 cm s -1. What is its wavelength in angstroms (Å)?a. 1.45b. 9.72x10 -8c. 3.25x10 -9d. 2.91e. 0.970

The smallest atoms can themselves exhibit quantum-mechanical behavior. Calculate the de Broglie wavelength (in pm) of a hydrogen atom traveling at 475 m/s.

What is the wavelength of a He atom traveling at 1.96 x10 3 m/sec?(mass of He = 6.65 x10 -27 kg)

Use the de Broglie relationship to determine the wavelengths of the following objects: (a) an 85-kg person skiing at 50 km/hr

As the velocity of an object doubles, what is expected of its deBroglie wavelength of the object?
A. It will increase by a factor of four
B. It will increase by a factor of two
C. It will remain constant
D. It will decrease by a factor of two
E. It will decrease by a factor of four

Use the de Broglie relationship to determine the wavelengths of the following objects: (b) a 10.0-g bullet fired at 250 m/s

Use the de Broglie relationship to determine the wavelengths of the following objects: (c) a lithium atom moving at 2.5 x 105 m/s

Use the de Broglie relationship to determine the wavelengths of the following objects: (d) an ozone (O3) molecule in the upper atmosphere moving at 550 m/s.

Among the elementary subatomic particles of physics is the muon, which decays within a few nanoseconds after formation. The muon has a rest mass 206.8 times that of an electron. Calculate the de Broglie wavelength associated with a muon traveling at a velocity of 8.85 x 105 cm/s.

Neutron diffraction is an important technique for determining the structures of molecules. Calculate the velocity of a neutron needed to achieve a wavelength of 0.955 Å. (Refer to the inside cover for the mass of the neutron).

The deBroglie wavelengths of a moving electron are given. Which wavelength would correspond to the greatest speed of the moving electron?a. 8.25 x 10 9 mb. 1.35 x 10 -13 mc. 8.25 x 10 12 md. 1.21 x 10 -6 me. 1.21 x 10 -10 m

The electron microscope has been widely used to obtain highly magnified images of biological and other types of materials. When an electron is accelerated through a particular potential field, it attains a speed of 8.95 x 106 m/s. What is the characteristic wavelength of this electron? Is the wavelength comparable to the size of atoms?

A certain rifle bullet has a mass of 6.93 g. Calculate the de Broglie wavelength of the bullet traveling at 1025 miles per hour. A= ___m

What is the de Broglie wavelength of a bowling ball rolling down a bowling alley lane? Assume the mass of the ball is 4500 g and it is moving at 4.12 m/s.1. 1.4725 x 10–37 m2. 1.229 x 10–32 m3. 3.57389 x 10–35 m4. 3.574 x 10–38 m

What is the wavelength of a neutron traveling at 4.15 km/day? [1J = 1 kg m 2 /s 2 ; mass of neutron = 1.675×10 −24 g; h = 6.63 x10 -34 J s; 1 km=1000 m]

An electron is traveling at a speed of 3.00 x 105 m/s. What is its de Broglie wavelength?
a) 0.64 nm
b) 1.87 nm
c) 2.42 nm
d) 4.31 nm
e) Electrons do not have detectable wavelengths.

The fastest serve in tennis is about 140 miles per hour, or about 63.2 m/s. Calculate the wavelength associated with an electron moving at this same velocity. (Mass of an electron = 9.11 x 10–31 kg)

What is the de Broglie wavelength (in meters) of a pitched baseball with a mass of 0.120 kg and a speed of 44.7 m/s? (1 J = 1 kg•m2/s2)A. 6.24 x 10-34 mB. 1.50 x 10-36 mC 1.24 x 10-34 mD. 0.76 x 10-34 mE. 6.24 x 10-36 m

In an explanation for the quantized energy levels of atoms de Broglie theorized that orbiting electrons might be at a fixed distance from the nucleus and thus only certain wavelength of wavelike motion would be stable. What is the implication of de Broglie's theory on the movement of matter? (a) Matter does not behave as though it moves in a wave. (b) All matter behaves as though it moves in a wave. (c) Only very fast moving matter behaves as though it moves in a wave. (d) Only very low mass matter behaves as though it moves in a wave. (e) Only very high matter behaves as though it moves in a wave.

The mass of an electron is 9.11x10 -31 kg . If the de Broglie wavelength for an electron in a hydrogen atom is 3.31x10-10 m , how fast is the electron moving relative to the speed of light? The speed of light is 3.00 x 108 m/s . Express your answer numerically as a percentage of the speed of light.

The mass of a golf ball is 45.9 g. If it leaves the tee with a speed of 69.0m/s, what is its corresponding wavelength? Express your answer numerically in meters.

What is the wavelength of a neutron traveling at 4.15 km/s? [1J = 1 kg m 2 /s2; mass of neutron = 1.675×10−24 g; h = 6.63 x10 -34 J s; 1 km=1000 m]

The faster an electron is moving, the __________ its kinetic energy, and the __________ its wavelength.(A) higher, shorter(B) higher, longer(C) lower, longer(D) lower, shorter(E) More than one of the answer choices will result in a true statement.

Consider an atom travelling at 1% the speed of light. The de Broglie wavelength is found to be 3.32 x 10-3 pm. Which element is this?A.) HB.) CaC.) BeD.) PE.) F

What is the wavelength of a marble (5 g) traveling at 372,889 m/s.

In a scanning electron microscope the wavelength of the electrons used to image very small objects is 2.74 pm, what is the velocity of the electron in the instrument? (h = 6.63 x 10 -34 kg•m2/sec; 1.00 pm = 1.00x10 -12 m, me = 9.11x10 -31 kg; 1J = 1Kg•m2/sec2)

What is the velocity of an electron that has a de Broglie
wavelength approximately the length of a chemical bond? Assume the length of a
chemical bond is 1.8×10−10 m . (The mass of an electron is 9.11 x 10-31 kg.)

In order for a thermonuclear fusion reaction of two deuterons (12H+ ) to take place, the deuterons must collide and each must have a velocity of about 1 x 106 m/s. Find the wavelength of such a deuteron.

For any microscope, the size of the smallest observable object is one-half the wavelength of the radiation used. For example, the smallest object observable with 400-nm light is 2 x 10−7 m. What is the smallest observable object for an electron microscope using electrons moving at 3.0 x 107 m/s?

Calculate the de Broglie wavelength of a 143-g baseball traveling at 90 mph.

In a technique used for surface analysis called auger electron spectroscopy (AES), electrons are accelerated toward a metal surface. These electrons cause the emissions of secondary electrons-called auger electrons-from the metal surface. The kinetic energy of the auger electrons depends on the composition of the surface. The presence of oxygen atoms on the surface results in auger electrons with a kinetic energy of approximately 510 eV. What is the de Broglie wavelength of this electron? [KE = mv2; 1 electron volt (eV) = 1.602 x 10-19 J]

Find the longest wavelength of a wave that can travel around in a circular orbit of radius 5.6 m.

A 0.22 caliber handgun fires a 29 g bullet at a velocity of 775 m/s.a. Calculate the de Broglie wavelength of the bullet.b. Is the wave nature of matter significant for bullets?

An alpha particle (mass = 6.6 x 10 −24 g) emitted by a radium isotope travels at 3.4 x 107 ± 0.1 x 10 7 mi/h. What is its de Broglie wavelength (in meters)?

Determine the mass of a ball with a wavelength of 3.45 x 10-34 m and a velocity of 6.55 m/s?

A certain rifle bullet has a mass of 8.85 g. Calculate the de Broglie wavelength (m) of the bullet traveling at 1769 miles per hour.

The de Broglie wavelength of an electron with a velocity of 7.40 × 106 m/s is ________ m. The mass of the electron is 9.11 × 10-28 g. A) 1.02 × 1010 B) 9.83 × 10-14 C) 1.02 × 1013 D) 9.83 × 10-17 E) 9.83 × 10-11

How to calculate the de Broglie wavelength for each of the following? a. an electron with a velocity 10.% of the speed of light b. a tennis ball (55 g) served at 35 m/s (,80 mi/h)

The de Broglie wavelength of a 455 kg car is found to be 5.43 × 10 –47 nm. Calculate the speed (m/s) of the car.a) 26.8 m/sb) 37.3 m/sc) 2.68 × 1019 m/sd) 3.73 × 107 m/se) 3.00 × 108 m/s

The deBroglie wavelengths of a moving electron are given. Which wavelength would correspond to the greatest speed of the moving electron?a. 8.25 x 10 9 mb. 1.35 x 10 -13 mc. 8.25 x 10 12 md. 1.21 x 10 -6 me. 1.21 x 10 -10 m

Since quantum-mechanical theory is universal, it applies to all objects, regardless of size. Therefore, according to the de Broglie relation, a thrown baseball should also exhibit wave properties. Why don’t we observe such properties at the ballpark?

How to calculate the wavelength of a baseball (m = 155 g) moving at 32.5 m/s?

The mass of an electron is 9.11 × 10− 31 kg. If the de Broglie wavelength for an electron in a hydrogen atom is 3.31 × 10− 10 m, how fast is the electron moving relative to the speed of light? The speed of light is 3.00 × 108 m/s.Just as light waves have particle behavior, a moving particle has a wave nature. The faster the particle is moving, the higher its kinetic energy and the shorter its wavelength. The wavelength, λ, of a particle of mass mm, and moving at velocity v, is given by the de Broglie relationwhere h = 6.626 × 10− 34 J ⋅ s is Planck's constant.This formula applies to all objects, regardless of size, but the de Broglie wavelength of macro objects is miniscule compared to their size, so we cannot observe their wave properties. In contrast, the wave properties of subatomic particles can be seen in such experiments as diffraction of electrons by a metal crystal.

Calculate the wavelength of an electron (m = 9.11 x 10-28 g) moving at 3.66 x 106 m/s.a. 5.52 x 10-9 mb. 1.81 x 10-10 mc. 1.99 x 10-10 md. 5.03 x 10-10 me. 2.76 × 10-9 m

Titanium (6.94x10-19 J) and silicon (7.77x10-19 J) surfaces are irradiated with UV radiation with a wavelength of 215 nm. What is the wavelength of the electrons emitted by the titanium surface?

The de Broglie relation λ=h/p can be rewritten in terms of the wave number k as p=kℏ. Recall that wave number is defined by k=2π/λ.(a) Using the fact that λ=v/f, find the wave numbers k1 and k2 corresponding to frequencies f1 and f2. Express your answer as two expressions separated by a comma. Use f1, f2, v, and π.(b) Find an expression for the uncertainty Δk=k1−k2 in the wave number. Use your results from Part (a). Express your answer in terms of quantities given in Part (a).

Calculate the velocities of electrons with de Broglie wavelengths of 1.0 x 10 2 nm and 1.0 nm.

The de Broglie equation predicts that the wavelength (in m) of a proton (1.67 x 10-27 kg) moving at 1000 m/s is 1) 3.96 • 10-10 m 2) 2.52 • 109 m 3) 3.96 • 10-7 m 4) > 1010 m 5) 2.52 • 106 m

The mass of a golf ball is 45.9 g. If it leaves the tee with a speed of 68.0 m/s , what is its corresponding wavelength?Just as light waves have particle behavior, a moving particle has a wave nature. The faster the particle is moving, the higher its kinetic energy and the shorter its wavelength. The wavelength, λ, of a particle of mass mm, and moving at velocity v, is given by the de Broglie relationwhere h = 6.626 × 10− 34 J ⋅ s is Planck's constant.This formula applies to all objects, regardless of size, but the de Broglie wavelength of macro objects is miniscule compared to their size, so we cannot observe their wave properties. In contrast, the wave properties of subatomic particles can be seen in such experiments as diffraction of electrons by a metal crystal.

Why is the wave nature of matter not important for a baseball?

Compare the wavelengths of an electron (mass = 9.11 x 10 −31 kg) and a proton (mass = 1.67 x 10−27 kg), each having a speed of 3.4 x 10 6 m/s.

A particular monochromatic orange light source emits light with a wavelength of 602 nm. What is the energy of a photon emitted from this light source?

A particular monochromatic light source emits light with a frequency of 662 THz. What is the wavelength of the light emitted? What is the color of the light emitted?

What is the wavelength of a257 Rf nucleus moving at 225 km hr-1? Select one: a. 2.48 x 4-11 m b. 4 13 x 10-35 m c. 1.15 x 10-35 m d. 6.90 x 10-12 m

Some chemical reactions can be initiated by light that carries an energy of 419 kJ/mol. Only light less than a certain wavelength will initiate such reactions. What is the longest wavelength in nanometers that can deliver 419 kJ/mol? Convert the energy m kJ/mol to energy in J/photon. Use Planck's Equation to determine the frequency in hertz. Convert frequency to wavelength in nanometers h = 6.626 x 10^34 J

What is the wavelength of an electron that has a mass of 9.10938188 x 10 -31 kg and a velocity of 2.17 x 106 m/s? Give your answer in angstroms.

Calculate the maximum wavelength of light (in nm) required to ionize a single rubidium atom. The first ionization energy of Rb Is 403 kJ/mol.

For 532-nm visible light, calculate its frequency (v, Hz), wavenumber (v, cm-1), and photon energy (J). If a laser were produced at this frequency, what color of light would you observe?

What velocity would an electron (mass = 9.11 x 10-31 kg) need for its de Broglie wavelength to be that of red light (755 nm )?

What is the energy of 1 photon of frequency 3.50 x 10 14 Hz.(a) 5.28 x 1043 J (b) 2.32 x 10-19 J (c) 1.89 x 1019 J (d) 5.28 x 1017 J

A proton in a linear accelerator has a de Broglie wavelength of 131 pm. Part AWhat is the speed of the proton? Express your answer with the appropriate units.

A particular monochromatic cyan light source emits light with a frequency of 631 THz. What is the energy of a photon emitted from this light source?

Part A A heat lamp produces 26.0 watts of power at a wavelength of 7.1 μm.How many photons are emitted per second? (1 watt = 1J/s) Express your answer using two significant figures.

What is the wavelength (in nm) of light having a frequency of 8.8 x 10 13 Hz? What is the frequency (in Hz) of light having a wavelength of 5.82 x 102 nm?

A proton in a linear accelerator has a de Broglie wavelength of 161 pm. What is the speed of the proton? Express your answer with the appropriate units.

A 0.22-caliber handgun fires a 27-g bullet at a velocity of 775 m/s.Part ACalculate the de Broglie wavelength of the bullet. Express your answer in meters using two significant figures. Part BIs the wave nature of matter significant for bullets? • yes • no

The energy of a particular color of red light is 2.89 x 10 -22 photon. The wavelength of this light is __________ nanometers. (109 nm = 1 m)

A proton in a linear accelerator has a de Broglie wavelength of 154 pm. Part AWhat is the speed of the proton? Express your answer with the appropriate units.

The UV light that is responsible for tanning the skin falls in the 320-to 400-nm region. Calculate the total energy (in joules) absorbed by a person exposed to this radiation for 3.5 h, given that there are 2.0 x 1016 photons hitting Earth's surface per square centimeter per second over a 80-nm (320 to 400 nm) range and that the exposed body area is 0.45 m2. Assume that only half of the radiation is absorbed and the other half is reflected by the body. (Use an average wavelength of 360 nm in calculating the energy of a photon.)

A 232-lb fullback runs 40 yd at 19.8 ± 0.1 mi/h. What is his de Broglie wavelength (in meters)?

The resolution limit of a microscope is roughly equal to the wavelength of light used in producing the image. Electron microscopes use an electron beam (in place of photons) to produce much higher resolution images, about 0.23 nm in modern instruments. Assuming that the resolution of an electron microscope is equal to the de Broglie wavelength of the electrons used, to what speed must the electrons be accelerated to obtain a resolution of 0.23 nm?

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