Question 1

According to Heisenberg,as the uncertainty in the measurement of a particle's momentum is reduced by a factor of 2,by what factor is the uncertainty in that same particle's position changed?

Accepted Answer

Heisenberg's uncertainty principle states that the product of the uncertainties in the measurement of a particle's position and momentum is always greater than or equal to a constant value, known as Planck's constant. Mathematically, ∆x * ∆p ≥ h/4π.

If the uncertainty in the measurement of a particle's momentum is reduced by a factor of 2, this means that ∆p is divided by 2. Using the uncertainty principle, we can rearrange the equation to solve for ∆x:

∆x ≥ h/4π∆p

If ∆p is divided by 2, then ∆x is multiplied by 2 (since h/4π and ∆p are constants). This means that the uncertainty in the particle's position is changed by a factor of 2. Therefore, the answer is C) 2.

Question 2

The electron microscope's main advantage over the optical microscope is which of the following?

Accepted Answer

The main advantage of the electron microscope over the optical microscope is the higher resolution possible, allowing for the visualization of much smaller structures and details. The electron microscope uses a beam of electrons instead of light and has a higher power lens, which contributes to its ability to achieve higher resolution.

Question 3

If the measured momentum of an electron is 3.6 × 10−²⁷ kg⋅m/s with an uncertainty of 2.6 × 10−²⁹ kg⋅m/s,what is the minimum uncertainty in the position? (h = 6.63 × 10−³⁴ J⋅s)

Accepted Answer

The answer of If the measured momentum of an electron...

Question 4

Of photons of red,yellow,light,and blue light,which photons have the greatest energy?

Accepted Answer

Blue light has the shortest wavelength and highest frequency, which means it has the greatest energy among the given photons.

Question 5

The Compton wavelength,h/m_ec,equals 0.002 43 nm.In Compton scattering,what is the greatest shift,Δλ,in wavelength that can occur?

Accepted Answer

The greatest shift in wavelength, Δλ, that can occur in Compton scattering is equal to twice the Compton wavelength, which is given by the formula Δλ = 2 h/m_ec. This occurs when the photon is scattered backward, resulting in the maximum energy transfer from the photon to the electron.

Question 6

Due to the dual nature of light and matter,either can act in an experiment as if it is a wave or a particle.In which experiment is the wave aspect exhibited for matter?

Accepted Answer

The Davisson and Germer experiment showed that electrons can exhibit wave-like behavior when fired at a crystal. The crystal caused the electrons to diffract, creating an interference pattern similar to that seen with waves. Therefore, the wave aspect of matter is exhibited in this experiment.

Question 7

A proton and an electron each have the same de Broglie wavelength.(i)Which has the greater speed,and (ii)which has the greater kinetic energy?

Accepted Answer

The de Broglie wavelength formula is λ = h/p, where λ is the wavelength, h is Planck's constant, and p is momentum. Since momentum p = mv (mass times velocity), for the same wavelength, a smaller mass (electron) must have a higher velocity than a larger mass (proton). For kinetic energy, KE = 1/2 mv^2, the electron's higher velocity squared, despite its smaller mass, can result in greater kinetic energy.

Question 8

If an electron has a measured wavelength of 0.832 × 10−¹⁰ m,what is its kinetic energy? (h = 6.63 × 10−³⁴ J⋅s,1 eV = 1.6 × 10−¹⁹ J,and m_e = 9.11 × 10−³¹ kg)

Accepted Answer

The answer of If an electron has a measured wavelength...

Question 9

The Heisenberg uncertainty principle places restriction on the precision of simultaneously measuring both position and momentum.This principle can also be applied to the simultaneous measurement of two other variables,which are:

Accepted Answer

The Heisenberg uncertainty principle states that the uncertainty in measuring the position and momentum of a particle is inversely proportional to each other. This means that if you try to measure the position of a particle more precisely, the uncertainty in its momentum will increase and vice versa. Similarly, the uncertainty principle can also be applied to the simultaneous measurement of energy and time interval, where the uncertainty in measuring one is inversely proportional to the other. The other options of force and color, mass and charge, and torque and frequency do not have an inverse relationship with each other that would satisfy the Heisenberg uncertainty principle.

Question 10

Starting from rest,an electron accelerates through a potential difference of 51.6 V.What is its de Broglie wavelength? (h = 6.63 × 10−³⁴ J⋅s,m_e = 9.11 × 10−³¹ kg,and 1 eV = 1.60 × 10−¹⁹ J)

Accepted Answer

The de Broglie wavelength is given by the equation: 
lambda = h / sqrt(2*m*eV), where h is Planck's constant, m is the mass of the particle, eV is the energy of the particle in electron volts.

Substituting the given values, we get:
lambda = (6.63*10^-34 J.s)/sqrt(2*9.11*10^-31 kg*51.6*1.60*10^-19 J)
= 1.7*10^-10 m
Therefore, the de Broglie wavelength of the electron is 1.7*10^-10 m (Option C).

Question 11

What is the energy of a photon that has the same wavelength as a 11.4-eV electron? (h = 6.63 × 10−³⁴ J⋅s,m_e = 9.11 × 10^-31 kg,1 eV = 1.6 × 10^-19 J)

Accepted Answer

The answer of What is the energy of a photon...

Question 12

The "seeing" ability or resolution of radiation is determined by its wavelength.If the size of an atom is approximately 1.3 × 10−¹⁰ m,how fast must an electron travel to have a wavelength smaller than that of an atom? (m_e = 9.11 × 10−³¹ kg and h = 6.63 × 10−³⁴ J⋅s)

Accepted Answer

To determine the velocity of an electron required for its wavelength to be smaller than the size of an atom, we use the de Broglie wavelength formula: λ = h / (mv), where λ is the wavelength, h is Planck's constant (6.63 × 10^-34 J⋅s), m is the mass of the electron (9.11 × 10^-31 kg), and v is the velocity of the electron. Rearranging the formula to solve for v gives us v = h / (mλ). Given that λ must be smaller than the size of an atom (~1.3 × 10^-10 m), we choose a value for λ just smaller than this size to ensure the electron's wavelength is indeed smaller. Substituting the given values into the rearranged formula and solving for v will yield a result that matches choice A, 5.6E+6 m/s, as the required velocity.

Question 13

A proton (mass = 1.67 × 10−²⁷ kg)has a kinetic energy of 2.4 MeV.If its momentum is measured with an uncertainty of 1.18%,what is the minimum uncertainty in its position? (h = 6.63 × 10−³⁴ J⋅s and 1 eV = 1.6 × 10−¹⁹ J)

Accepted Answer

The answer of A proton (mass = 1.67 × 10−²⁷...

Question 14

If a ¹H nucleus,a ²H nucleus,and a ³H nucleus all had the same momentum,which one has the greatest de Broglie wavelength?

Accepted Answer

The answer of If a ¹H nucleus,a ²H nucleus,and a...

Question 15

The uncertainty principle was derived by whom?

Accepted Answer

The uncertainty principle was derived by Werner Heisenberg in 1927.

Question 16

That light has a dual nature is referring to light:

Accepted Answer

Light exhibits both wave-like and particle-like behavior, which is known as wave-particle duality. This means that light can be described as both a wave and a particle (or photon).

Question 17

The de Broglie wavelength of a 0.069 kg golf ball is 4.67 × 10−³⁴m.What is its speed? (h = 6.63 × 10−³⁴ J⋅s)

Accepted Answer

The de Broglie wavelength (λ) of an object is given by:
λ = h/p
where h is Planck's constant and p is the momentum of the object.

We can rearrange this equation to solve for the momentum:
p = h/λ

Then, we can use the definition of momentum to solve for the speed:
p = mv
where m is the mass of the object and v is its velocity.

Rearranging this equation gives:
v = p/m = h/(mλ)

Substituting in the given values, we get:
v = (6.63 × 10^-34 J·s) / (0.069 kg × 4.67 × 10^-31 m) = 21 m/s

Therefore, the best choice is B: 21 m/s.

Question 18

An electron microscope operates with electrons of kinetic energy 58 keV.What is the wavelength of these electrons? Assume this speed is not relativistic.(h = 6.63 × 10−³⁴ J⋅s,c = 3.00 × 10⁸ m/s,1 eV = 1.60 × 10−¹⁹ J,and m_e = 9.11 × 10−³¹ kg)

Accepted Answer

The answer of An electron microscope operates with electrons of...

Question 19

The wave function as derived in Schrödinger's equation is best described as being a measure of which of the following?

Accepted Answer

The wave function in Schrödinger's equation represents the probability amplitude of finding a particle in a particular state or location. Therefore, the wave function is best described as a measure of probability.

Quiz 27: Quantum Physics Blackbody Radiation and Plancks Hypothesis

According to Heisenberg,as the uncertainty in the measurement of a particle's momentum is reduced by a factor of 2,by what factor is the uncertainty in that same particle's position changed?

The electron microscope's main advantage over the optical microscope is which of the following?

If the measured momentum of an electron is 3.6 × 10−²⁷ kg⋅m/s with an uncertainty of 2.6 × 10−²⁹ kg⋅m/s,what is the minimum uncertainty in the position? (h = 6.63 × 10−³⁴ J⋅s)

Of photons of red,yellow,light,and blue light,which photons have the greatest energy?

The Compton wavelength,h/m_ec,equals 0.002 43 nm.In Compton scattering,what is the greatest shift,Δλ,in wavelength that can occur?

Due to the dual nature of light and matter,either can act in an experiment as if it is a wave or a particle.In which experiment is the wave aspect exhibited for matter?

A proton and an electron each have the same de Broglie wavelength.(i) Which has the greater speed,and (ii) which has the greater kinetic energy?

If an electron has a measured wavelength of 0.832 × 10−¹⁰ m,what is its kinetic energy? (h = 6.63 × 10−³⁴ J⋅s,1 eV = 1.6 × 10−¹⁹ J,and m_e = 9.11 × 10−³¹ kg)

The Heisenberg uncertainty principle places restriction on the precision of simultaneously measuring both position and momentum.This principle can also be applied to the simultaneous measurement of two other variables,which are:

Starting from rest,an electron accelerates through a potential difference of 51.6 V.What is its de Broglie wavelength? (h = 6.63 × 10−³⁴ J⋅s,m_e = 9.11 × 10−³¹ kg,and 1 eV = 1.60 × 10−¹⁹ J)

What is the energy of a photon that has the same wavelength as a 11.4-eV electron? (h = 6.63 × 10−³⁴ J⋅s,m_e = 9.11 × 10^-31 kg,1 eV = 1.6 × 10^-19 J)

The "seeing" ability or resolution of radiation is determined by its wavelength.If the size of an atom is approximately 1.3 × 10−¹⁰ m,how fast must an electron travel to have a wavelength smaller than that of an atom? (m_e = 9.11 × 10−³¹ kg and h = 6.63 × 10−³⁴ J⋅s)

A proton (mass = 1.67 × 10−²⁷ kg) has a kinetic energy of 2.4 MeV.If its momentum is measured with an uncertainty of 1.18%,what is the minimum uncertainty in its position? (h = 6.63 × 10−³⁴ J⋅s and 1 eV = 1.6 × 10−¹⁹ J)

If a ¹H nucleus,a ²H nucleus,and a ³H nucleus all had the same momentum,which one has the greatest de Broglie wavelength?

The uncertainty principle was derived by whom?

That light has a dual nature is referring to light:

The de Broglie wavelength of a 0.069 kg golf ball is 4.67 × 10−³⁴m.What is its speed? (h = 6.63 × 10−³⁴ J⋅s)

An electron microscope operates with electrons of kinetic energy 58 keV.What is the wavelength of these electrons? Assume this speed is not relativistic.(h = 6.63 × 10−³⁴ J⋅s,c = 3.00 × 10⁸ m/s,1 eV = 1.60 × 10−¹⁹ J,and m_e = 9.11 × 10−³¹ kg)

The wave function as derived in Schrödinger's equation is best described as being a measure of which of the following?

Quiz 27: Quantum Physics Blackbody Radiation and Plancks Hypothesis

According to Heisenberg,as the uncertainty in the measurement of a particle's momentum is reduced by a factor of 2,by what factor is the uncertainty in that same particle's position changed?

The electron microscope's main advantage over the optical microscope is which of the following?

If the measured momentum of an electron is 3.6 × 10−27 kg⋅m/s with an uncertainty of 2.6 × 10−29 kg⋅m/s,what is the minimum uncertainty in the position? (h = 6.63 × 10−34 J⋅s)

Of photons of red,yellow,light,and blue light,which photons have the greatest energy?

The Compton wavelength,h/mec,equals 0.002 43 nm.In Compton scattering,what is the greatest shift,Δλ,in wavelength that can occur?

Due to the dual nature of light and matter,either can act in an experiment as if it is a wave or a particle.In which experiment is the wave aspect exhibited for matter?

A proton and an electron each have the same de Broglie wavelength.(i) Which has the greater speed,and (ii) which has the greater kinetic energy?

If an electron has a measured wavelength of 0.832 × 10−10 m,what is its kinetic energy? (h = 6.63 × 10−34 J⋅s,1 eV = 1.6 × 10−19 J,and me = 9.11 × 10−31 kg)

The Heisenberg uncertainty principle places restriction on the precision of simultaneously measuring both position and momentum.This principle can also be applied to the simultaneous measurement of two other variables,which are:

Starting from rest,an electron accelerates through a potential difference of 51.6 V.What is its de Broglie wavelength? (h = 6.63 × 10−34 J⋅s,me = 9.11 × 10−31 kg,and 1 eV = 1.60 × 10−19 J)

What is the energy of a photon that has the same wavelength as a 11.4-eV electron? (h = 6.63 × 10−34 J⋅s,me = 9.11 × 10-31 kg,1 eV = 1.6 × 10-19 J)

The "seeing" ability or resolution of radiation is determined by its wavelength.If the size of an atom is approximately 1.3 × 10−10 m,how fast must an electron travel to have a wavelength smaller than that of an atom? (me = 9.11 × 10−31 kg and h = 6.63 × 10−34 J⋅s)

A proton (mass = 1.67 × 10−27 kg) has a kinetic energy of 2.4 MeV.If its momentum is measured with an uncertainty of 1.18%,what is the minimum uncertainty in its position? (h = 6.63 × 10−34 J⋅s and 1 eV = 1.6 × 10−19 J)

If a 1H nucleus,a 2H nucleus,and a 3H nucleus all had the same momentum,which one has the greatest de Broglie wavelength?

The uncertainty principle was derived by whom?

That light has a dual nature is referring to light:

The de Broglie wavelength of a 0.069 kg golf ball is 4.67 × 10−34m.What is its speed? (h = 6.63 × 10−34 J⋅s)

An electron microscope operates with electrons of kinetic energy 58 keV.What is the wavelength of these electrons? Assume this speed is not relativistic.(h = 6.63 × 10−34 J⋅s,c = 3.00 × 108 m/s,1 eV = 1.60 × 10−19 J,and me = 9.11 × 10−31 kg)

The wave function as derived in Schrödinger's equation is best described as being a measure of which of the following?

If the measured momentum of an electron is 3.6 × 10−²⁷ kg⋅m/s with an uncertainty of 2.6 × 10−²⁹ kg⋅m/s,what is the minimum uncertainty in the position? (h = 6.63 × 10−³⁴ J⋅s)

The Compton wavelength,h/m_ec,equals 0.002 43 nm.In Compton scattering,what is the greatest shift,Δλ,in wavelength that can occur?

If an electron has a measured wavelength of 0.832 × 10−¹⁰ m,what is its kinetic energy? (h = 6.63 × 10−³⁴ J⋅s,1 eV = 1.6 × 10−¹⁹ J,and m_e = 9.11 × 10−³¹ kg)

Starting from rest,an electron accelerates through a potential difference of 51.6 V.What is its de Broglie wavelength? (h = 6.63 × 10−³⁴ J⋅s,m_e = 9.11 × 10−³¹ kg,and 1 eV = 1.60 × 10−¹⁹ J)

What is the energy of a photon that has the same wavelength as a 11.4-eV electron? (h = 6.63 × 10−³⁴ J⋅s,m_e = 9.11 × 10^-31 kg,1 eV = 1.6 × 10^-19 J)

The "seeing" ability or resolution of radiation is determined by its wavelength.If the size of an atom is approximately 1.3 × 10−¹⁰ m,how fast must an electron travel to have a wavelength smaller than that of an atom? (m_e = 9.11 × 10−³¹ kg and h = 6.63 × 10−³⁴ J⋅s)

A proton (mass = 1.67 × 10−²⁷ kg) has a kinetic energy of 2.4 MeV.If its momentum is measured with an uncertainty of 1.18%,what is the minimum uncertainty in its position? (h = 6.63 × 10−³⁴ J⋅s and 1 eV = 1.6 × 10−¹⁹ J)

If a ¹H nucleus,a ²H nucleus,and a ³H nucleus all had the same momentum,which one has the greatest de Broglie wavelength?

The de Broglie wavelength of a 0.069 kg golf ball is 4.67 × 10−³⁴m.What is its speed? (h = 6.63 × 10−³⁴ J⋅s)

An electron microscope operates with electrons of kinetic energy 58 keV.What is the wavelength of these electrons? Assume this speed is not relativistic.(h = 6.63 × 10−³⁴ J⋅s,c = 3.00 × 10⁸ m/s,1 eV = 1.60 × 10−¹⁹ J,and m_e = 9.11 × 10−³¹ kg)