Question 1

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 more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. This principle can also be applied to other pairs of variables, the most notable being energy and time interval. The more precisely we know the energy of a particle, the less precisely we can know the time interval over which that energy is measured, and vice versa. Therefore, choice B is the best choice as it correctly identifies two variables that can be subject to the Heisenberg uncertainty principle.

Question 2

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 3

Light with wavelength 5.6 * 10^-7 is used to determine the position of an electron to within the wavelength of the light.What is the resulting uncertainty in the electron's velocity? h = 6.63 *10^-34 J.s,m_e = 9.11 * 10^-31 kg

Accepted Answer

The uncertainty principle states that ΔxΔp ≥ h/4π, where Δx is the uncertainty in position and Δp is the uncertainty in momentum. We know that Δx = wavelength of light = 5.6 x 10^-7 m. To find Δp, we can use the equation p = mv, where m is the mass of the electron and v is its velocity. Rearranging, we get v = p/m. We want to find the uncertainty in velocity, so we need to find Δv.

From the equation ΔxΔp ≥ h/4π, we can solve for Δp: 
Δp ≥ h/(4πΔx) 
Δp ≥ (6.63 x 10^-34 J s)/(4π x 5.6 x 10^-7 m) 
Δp ≥ 2.37 x 10^-27 kg m/s

Now we can find Δv: 
Δv = Δp/m 
Δv = (2.37 x 10^-27 kg m/s)/(9.11 x 10^-31 kg) 
Δv = 260.5 m/s

Therefore, the resulting uncertainty in the electron's velocity is approximately 260 m/s. The closest answer choice is B, 103 m/s.

Question 4

The uncertainty principle was derived by whom?

Accepted Answer

The uncertainty principle in quantum mechanics was derived by Werner Heisenberg.

Question 5

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 6

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.

Question 7

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 8

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 de Broglie wavelength is inversely proportional to the momentum of the particle. Since all three nuclei have the same momentum, they all have the same de Broglie wavelength.

Question 9

An electron and an alpha particle (a helium-4 nucleus)each have the same non-relativistic speed.Which has the greatest kinetic energy,and which has the shortest de Broglie wavelength?

Accepted Answer

The kinetic energy of a particle is given by the formula: 
KE = (1/2)mv^2 
where m is the mass of the particle and v is its velocity. 
Since the alpha particle has a much greater mass than the electron, it will have a much greater kinetic energy at the same speed.

The de Broglie wavelength of a particle is given by the formula: 
λ = h/p 
where h is Planck's constant and p is the momentum of the particle. 
Since the momentum of a particle is given by p = mv, the de Broglie wavelength is proportional to the mass and inversely proportional to the velocity. 
Therefore, the electron with its smaller mass will have a shorter de Broglie wavelength than the alpha particle at the same velocity.

Question 10

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 11

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 of an electron is given by the expression:

λ = h/p

where h is the Planck's constant and p is the momentum of the electron.

The momentum of an electron accelerated through a potential difference V is given by the expression:

p = sqrt(2m*eV)

where m is the mass of the electron and e is the charge of an electron.

Substituting the given values, we get:

p = sqrt(2*9.11E-31*1.60E-19*51.6) = 5.978E-23 kg.m/s

Now, we can calculate the de Broglie wavelength as:

λ = h/p = 6.63E-34/5.978E-23 = 1.111E-10 m = 1.1E-10 m (approx)

Therefore, the correct choice is C.

Question 12

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 13

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 uncertainties in a particle's position and momentum is constant. Mathematically, Δx * Δp ≥ h/4π, where Δx is the uncertainty in position, Δp is the uncertainty in momentum, and h is Planck's constant. If Δp is reduced by a factor of 2, then it becomes Δp/2. We can rearrange the above equation to solve for Δx: Δx ≥ h/4πΔp. If Δp is reduced by a factor of 2, then Δx must be doubled to maintain the same minimum uncertainty according to the inequality. Therefore, the uncertainty in position changes by a factor of 2.

Question 14

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...

Quiz 27: Quantum Physics

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

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?

Light with wavelength 5.6 * 10^-7 is used to determine the position of an electron to within the wavelength of the light.What is the resulting uncertainty in the electron's velocity? h = 6.63 10^-34 J.s,m_e = 9.11 10^-31 kg

The uncertainty principle was derived by whom?

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?

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)

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

An electron and an alpha particle (a helium-4 nucleus) each have the same non-relativistic speed.Which has the greatest kinetic energy,and which has the shortest de Broglie wavelength?

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)

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?

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)

Quiz 27: Quantum Physics

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

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?

​Light with wavelength 5.6 * 10-7 is used to determine the position of an electron to within the wavelength of the light.What is the resulting uncertainty in the electron's velocity? h = 6.63 *10-34 J.s,me = 9.11 * 10-31 kg

The uncertainty principle was derived by whom?

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?

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)

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

An electron and an alpha particle (a helium-4 nucleus) each have the same non-relativistic speed.Which has the greatest kinetic energy,and which has the shortest de Broglie wavelength?

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)

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)

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?

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)

Light with wavelength 5.6 * 10^-7 is used to determine the position of an electron to within the wavelength of the light.What is the resulting uncertainty in the electron's velocity? h = 6.63 10^-34 J.s,m_e = 9.11 10^-31 kg

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 "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)

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

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)

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)