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

According to Heisenberg's uncertainty principle, the product of the uncertainty in a particle's position and momentum is always greater than or equal to h/4π. Mathematically, Δx*Δp >= h/4π. Thus, if the uncertainty in a particle's momentum is reduced by a factor of 2, then Δp becomes Δp/2. In order to maintain the equality, the uncertainty in the particle's position must increase by a factor of 2. Thus, Δx becomes 2Δx, or a factor of 2. Therefore, the answer is C, or 2.

Question 2

A proton (mass = 1.67 x 10^-27kg)has a kinetic energy of 1.00 MeV.If its momentum is measured with an uncertainty of 1.00%,what is the minimum uncertainty in its position? (h = 6.63 x 10^-34 J*s and 1 eV = 1.6 x 10^-19 J)

Accepted Answer

We can use the Heisenberg Uncertainty Principle: 
Δx * Δp ≥ h/4π 
where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is Planck's constant. 
First, we need to convert the kinetic energy of the proton into momentum: 
K.E. = p²/2m 
1.00 MeV = p²/2(1.67 x 10^-27 kg) 
p ≈ 1.91 x 10^-19 kg m/s 
Now, we can calculate the uncertainty in momentum: 
Δp = 1.00% * p 
Δp ≈ 1.91 x 10^-21 kg m/s 
Finally, we can calculate the minimum uncertainty in position: 
Δx ≥ h/4πΔp 
Δx ≥ (6.63 x 10^-34 J s)/(4π(1.91 x 10^-21 kg m/s)) 
Δx ≥ 2.28 x 10^-13 m 
Therefore, the answer is B, with a minimum uncertainty in position of 2.28 x 10^-13 m.

Question 3

Surface #1 has work function  ,and when bombarded with photons of wavelength  emits photoelectrons with maximum energy  .Surface #2 has work function  ,and when bombarded by photons of wavelength  emits photoelectrons with maximum energy  .If  ,then which of the following must be true?

Accepted Answer

The equation relating the maximum kinetic energy of a photoelectron and the work function of a surface is:
KEmax = hν - Φ
where h is Planck's constant, ν is the frequency of the incident photon, and Φ is the work function of the surface.

For Surface #1,
hν = hc/λ = (6.62607004 × 10^-34 J s)(2.9979 x 10^8 m/s)/(11eaa64f_8f99_f44f_a696_1deb2fa5bed9_TB5258_11) = 1.791 x 10^-16 J
KEmax = (11eaa64f_8f9a_1b60_a696_8d064645cf6c_TB5258_11)
Φ = (11eaa64f_8f99_cd3e_a696_b54c5af9a301_TB5258_11)

Solving for hν in terms of KEmax and Φ, we get:
hν = KEmax + Φ = (11eaa64f_8f9a_1b60_a696_8d064645cf6c_TB5258_11) + (11eaa64f_8f99_cd3e_a696_b54c5af9a301_TB5258_11) = (11eaa64f_8f9b_53e9_a696_d32469a93a71_TB5258_11)

For Surface #2,
hν = hc/λ = (6.62607004 × 10^-34 J s)(2.9979 x 10^8 m/s)/(11eaa64f_8f9a_6982_a696_351af9537f82_TB5258_11) = 1.124 x 10^-16 J
KEmax = (11eaa64f_8f9a_9093_a696_eb0ab6224284_TB5258_11)
Φ = (11eaa64f_8f9a_4271_a696_27bba5f2fc42_TB5258_11)

Solving for hν in terms of KEmax and Φ, we get:
hν = KEmax + Φ = (11eaa64f_8f9a_9093_a696_eb0ab6224284_TB5258_11) + (11eaa64f_8f9a_4271_a696_27bba5f2fc42_TB5258_11) = (11eaa64f_8f9b_7afa_a696_8921bf465bbe_TB5258_11)

Comparing the two values of hν, we see that (11eaa64f_8f9b_7afa_a696_8921bf465bbe_TB5258_11) is greater than (11eaa64f_8f9b_53e9_a696_d32469a93a71_TB5258_11). This means that the frequency of the incident photon required to produce photoelectrons with the same maximum kinetic energy is greater for Surface #2 than for Surface #1. Therefore, the threshold frequency for Surface #2 must be greater than the threshold frequency for Surface #1.

Choice D is the only option that correctly compares the threshold frequencies of the two surfaces.

Question 4

The de Broglie wavelength of a 0.060 kg golf ball is 4.28 x 10^-34m.What is its speed? (h = 6.63 x 10^-34 J*s)

Accepted Answer

The de Broglie wavelength is given by the equation:

λ = h / (mv)

where λ is the de Broglie wavelength, h is the Planck constant, m is the mass of the particle, v is its velocity.

Rearranging the equation, we get:

v = h / (mλ)

Substituting the given values, we get:

v = 6.63 x 10^-34 J s / (0.060 kg x 4.28 x 10^-34 m) = 26.3 m/s

Therefore, the answer is B) 26 m/s

Question 5

An electron microscope operates with electrons of kinetic energy 50.0 keV.What is the wavelength of these electrons? Assume this speed is not relativistic.(h = 6.63 x 10^-34 J*s,c = 3.00 x 10⁸ m/s,1 eV = 1.60 x 10^-19 J,and m_e = 9.11 x 10^-31 kg)

Accepted Answer

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

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 demonstrated the wave-like behavior of electrons, which are a form of matter.

Question 7

What is the energy of a photon that has the same wavelength as a 12-eV electron? (h = 6.63 x 10^-34 J*s)

Accepted Answer

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

Question 8

What is the de Broglie wavelength for a proton (m = 1.67 x 10^-27kg)moving at a speed of 6.0 x 10⁶ m/s? (h = 6.63 x 10^-34 J*s)

Accepted Answer

The de Broglie wavelength is calculated using the formula λ = h / (mv). Substituting the given values: λ = 6.63 x 10^-34 J·s / (1.67 x 10^-27 kg * 6.0 x 10^6 m/s) = 0.66 x 10^-13 m.

Question 9

If the measured momentum of an electron is 3.20 x 10^-27 kg*m/s with an uncertainty of 1.6 x 10^-29kg*m/s,what is the minimum uncertainty in the position? (h = 6.63 x 10^-34 J*s)

Accepted Answer

The uncertainty principle states that ΔxΔp ≥ h/4π. 
Using the given values, we can calculate the uncertainty in position:

Δp = 1.6 x 10^-29 kg·m/s 
p = 3.20 x 10^-27 kg·m/s

Δx ≥ h/(4πΔp) = 3.3 x 10^-6 m

Therefore, the minimum uncertainty in position is 3.3 x 10^-6 m, which corresponds to choice B.

Question 10

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

Accepted Answer

The answer of The Compton wavelength,h/m_ec,equals 0.002 43 nm.In Compton...

Question 11

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 there is a fundamental limit to the precision with which position and momentum of a particle can be known simultaneously. This principle can also be generalized to other pairs of variables, such as energy and time interval. The uncertainty principle places a limit on the precision with which both of these variables can be known at the same time, giving rise to the famous inequality ΔE Δt ≥ ħ/2. The other options, force and color or torque and frequency, are not related pairs of variables and are therefore not subject to the Heisenberg uncertainty principle. Mass and charge are related, but there is no Heisenberg uncertainty principle for these quantities.

Question 12

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, as derived in Schrödinger's equation, is a complex-valued function that describes the probability density of a particle at a given position in space and time. Therefore, the wave function is a measure of probability. It does not directly measure photon frequency or wavelength, nor does it measure particle wavelength as a direct physical property.

Question 13

If an electron has a measured wavelength of 0.850 x 10^-10 m,what is its kinetic energy? (h = 6.63 x 10^-34 J*s,1 eV = 1.6 x 10^-19 J,and m_e = 9.11 x 10^-31 kg)

Accepted Answer

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

Question 14

That light has a dual nature is referring to light:

Accepted Answer

Light exhibits both wave-like and particle-like behavior, known as wave-particle duality. This means that it can behave as both waves and particles, depending on how it is being observed or measured.

Question 15

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

Accepted Answer

Blue light has the greatest energy among these options. This is because energy is directly proportional to the frequency of the light, and blue light has a higher frequency than red, yellow, or green light.

Question 16

Starting from rest,an electron accelerates through a potential difference of 40 V.What is its de Broglie wavelength? (h = 6.63 x 10^-34 J*s,m_e = 9.11 x 10^-31 kg,and 1 eV = 1.60 x 10^-19 J)

Accepted Answer

The answer of Starting from rest,an electron accelerates through a...

Question 17

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 18

The uncertainty principle was derived by whom?

Accepted Answer

The uncertainty principle was derived by Werner Heisenberg in 1927.

Question 19

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 its higher resolution, which allows for the visualization of much smaller structures. This is due to the fact that the electron microscope uses a beam of electrons rather than a beam of light, providing higher magnification and better resolution. It does not dispense with the need for a lens, as both microscopes use lenses to magnify the image. Portability is not a major advantage of the electron microscope.

Question 20

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

Accepted Answer

The de Broglie wavelength of an electron is given by λ = h/p, where p is the momentum of the electron. To have a wavelength smaller than that of an atom (10^-10 m), we need λ < 10^-10 m. Therefore, λ = h/p < 10^-10 m => p > h/10^-10 m = 6.63 x 10^-25 kg m/s The momentum of an electron is given by p = mv, where m is the mass of the electron and v is its speed. Therefore, v = p/m > (h/10^-10 m)/9.11 x 10^-31 kg => v > 7.27 x 10^6 m/s Therefore, the electron must travel at a speed greater than 7.27 x 10^6 m/s to have a wavelength smaller than that of an atom. The closest answer choice is A) 7.3 x 10^16 m/s.

Quiz 27: Quantum Physics

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?

A proton (mass = 1.67 x 10^-27kg) has a kinetic energy of 1.00 MeV.If its momentum is measured with an uncertainty of 1.00%,what is the minimum uncertainty in its position? (h = 6.63 x 10^-34 J*s and 1 eV = 1.6 x 10^-19 J)

Surface #1 has work function ,and when bombarded with photons of wavelength emits photoelectrons with maximum energy .Surface #2 has work function ,and when bombarded by photons of wavelength emits photoelectrons with maximum energy .If ,then which of the following must be true?

The de Broglie wavelength of a 0.060 kg golf ball is 4.28 x 10^-34m.What is its speed? (h = 6.63 x 10^-34 J*s)

An electron microscope operates with electrons of kinetic energy 50.0 keV.What is the wavelength of these electrons? Assume this speed is not relativistic.(h = 6.63 x 10^-34 J*s,c = 3.00 x 10⁸ m/s,1 eV = 1.60 x 10^-19 J,and m_e = 9.11 x 10^-31 kg)

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?

What is the energy of a photon that has the same wavelength as a 12-eV electron? (h = 6.63 x 10^-34 J*s)

What is the de Broglie wavelength for a proton (m = 1.67 x 10^-27kg) moving at a speed of 6.0 x 10⁶ m/s? (h = 6.63 x 10^-34 J*s)

If the measured momentum of an electron is 3.20 x 10^-27 kgm/s with an uncertainty of 1.6 x 10^-29kgm/s,what is the minimum uncertainty in the position? (h = 6.63 x 10^-34 J*s)

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

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:

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

If an electron has a measured wavelength of 0.850 x 10^-10 m,what is its kinetic energy? (h = 6.63 x 10^-34 J*s,1 eV = 1.6 x 10^-19 J,and m_e = 9.11 x 10^-31 kg)

That light has a dual nature is referring to light:

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

Starting from rest,an electron accelerates through a potential difference of 40 V.What is its de Broglie wavelength? (h = 6.63 x 10^-34 J*s,m_e = 9.11 x 10^-31 kg,and 1 eV = 1.60 x 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?

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

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

Quiz 27: Quantum Physics

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?

A proton (mass = 1.67 x 10-27 kg) has a kinetic energy of 1.00 MeV.If its momentum is measured with an uncertainty of 1.00%,what is the minimum uncertainty in its position? (h = 6.63 x 10-34 J*s and 1 eV = 1.6 x 10-19 J)

Surface #1 has work function ,and when bombarded with photons of wavelength emits photoelectrons with maximum energy .Surface #2 has work function ,and when bombarded by photons of wavelength emits photoelectrons with maximum energy .If ,then which of the following must be true?

The de Broglie wavelength of a 0.060 kg golf ball is 4.28 x 10-34m.What is its speed? (h = 6.63 x 10-34 J*s)

An electron microscope operates with electrons of kinetic energy 50.0 keV.What is the wavelength of these electrons? Assume this speed is not relativistic.(h = 6.63 x 10-34 J*s,c = 3.00 x 108 m/s,1 eV = 1.60 x 10-19 J,and me = 9.11 x 10-31 kg)

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?

What is the energy of a photon that has the same wavelength as a 12-eV electron? (h = 6.63 x 10-34 J*s)

What is the de Broglie wavelength for a proton (m = 1.67 x 10-27 kg) moving at a speed of 6.0 x 106 m/s? (h = 6.63 x 10-34 J*s)

If the measured momentum of an electron is 3.20 x 10-27 kg*m/s with an uncertainty of 1.6 x 10-29 kg*m/s,what is the minimum uncertainty in the position? (h = 6.63 x 10-34 J*s)

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

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:

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

If an electron has a measured wavelength of 0.850 x 10-10 m,what is its kinetic energy? (h = 6.63 x 10-34 J*s,1 eV = 1.6 x 10-19 J,and me = 9.11 x 10-31 kg)

That light has a dual nature is referring to light:

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

Starting from rest,an electron accelerates through a potential difference of 40 V.What is its de Broglie wavelength? (h = 6.63 x 10-34 J*s,me = 9.11 x 10-31 kg,and 1 eV = 1.60 x 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?

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

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

A proton (mass = 1.67 x 10^-27kg) has a kinetic energy of 1.00 MeV.If its momentum is measured with an uncertainty of 1.00%,what is the minimum uncertainty in its position? (h = 6.63 x 10^-34 J*s and 1 eV = 1.6 x 10^-19 J)

The de Broglie wavelength of a 0.060 kg golf ball is 4.28 x 10^-34m.What is its speed? (h = 6.63 x 10^-34 J*s)

An electron microscope operates with electrons of kinetic energy 50.0 keV.What is the wavelength of these electrons? Assume this speed is not relativistic.(h = 6.63 x 10^-34 J*s,c = 3.00 x 10⁸ m/s,1 eV = 1.60 x 10^-19 J,and m_e = 9.11 x 10^-31 kg)

What is the energy of a photon that has the same wavelength as a 12-eV electron? (h = 6.63 x 10^-34 J*s)

What is the de Broglie wavelength for a proton (m = 1.67 x 10^-27kg) moving at a speed of 6.0 x 10⁶ m/s? (h = 6.63 x 10^-34 J*s)

If the measured momentum of an electron is 3.20 x 10^-27 kgm/s with an uncertainty of 1.6 x 10^-29kgm/s,what is the minimum uncertainty in the position? (h = 6.63 x 10^-34 J*s)

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

If an electron has a measured wavelength of 0.850 x 10^-10 m,what is its kinetic energy? (h = 6.63 x 10^-34 J*s,1 eV = 1.6 x 10^-19 J,and m_e = 9.11 x 10^-31 kg)

Starting from rest,an electron accelerates through a potential difference of 40 V.What is its de Broglie wavelength? (h = 6.63 x 10^-34 J*s,m_e = 9.11 x 10^-31 kg,and 1 eV = 1.60 x 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 "seeing" ability or resolution of radiation is determined by its wavelength.If the size of an atom is approximately 10^-10 m,how fast must an electron travel to have a wavelength smaller than that of an atom? (m_e = 9.11 x 10^-31 kg and h = 6.63 x 10^-34 J*s)