Question 1

If the measured momentum of an electron is 3.20 *10^-²⁷ kg.m/s with an uncertainty of 4.8 *10^-²⁸kg.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 2

What is the energy of a photon that has the same wavelength as a 24 eV electron? (h = 6.63 *10^-³⁴ J.s, m_e = 9.11*10^-³¹ kg)

Accepted Answer

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

Question 3

That light has a dual nature is referring to light:

Accepted Answer

Light's dual nature refers to its ability to exhibit both wave-like and particle-like properties, known as wave-particle duality.

Question 4

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

Accepted Answer

According to Heisenberg's Uncertainty Principle, the product of the uncertainties in position and momentum is constant. If the uncertainty in momentum is increased by a factor of 2, the uncertainty in position must decrease by a factor of 1/2 to maintain the constant product.

Question 5

When  stands for Planck's constant, what does  (read as "h bar") stand for?

Accepted Answer

The answer of When  stands for Planck's constant, what...

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 nature of electrons by showing electron diffraction patterns, confirming that matter can exhibit wave-like behavior.

Question 7

A proton (mass = 1.67 *10 ^- ²⁷kg) has a kinetic energy of 1.00 MeV. If its momentum is measured with an uncertainty of 2.00%, 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 uncertainty in position is calculated using the Heisenberg Uncertainty Principle: Δx ≥ h / (4πΔp). The uncertainty in momentum Δp is 2% of the momentum p, which can be found from the kinetic energy. Converting 1 MeV to joules and using the relativistic energy-momentum relation, we find Δx.

Question 8

If an electron has a measured wavelength of 1.20 *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

When an electron is in a magnetic field, different spin states associated with the electron's magnetic moment will occur. What are these states called?

Accepted Answer

The spin states of an electron in a magnetic field are commonly referred to as "up" and "down," corresponding to the two possible orientations of the electron's spin relative to the magnetic field.

Question 10

Starting from rest, an electron accelerates through a potential difference of 67 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 answer of Starting from rest, an electron accelerates through...

Question 11

When electrons are placed in a magnetic field, their spin orientations are quantized. How many orientations with respect to the field may result?

Accepted Answer

Electrons in a magnetic field have two possible spin orientations with respect to the field: parallel or antiparallel.

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 in Schrödinger's equation represents the probability amplitude, and its square gives the probability density of finding a particle in a given space.

Question 13

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 14

In the STM, what are the S and T?

Accepted Answer

STM stands for Scanning Tunneling Microscope, where "S" is for Scanning and "T" is for Tunneling.

Question 15

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 *10^-³¹ kg and h = 6.63 *10^-³⁴ J.s)

Accepted Answer

To find the speed of the electron, use the de Broglie wavelength formula: λ = h / (m_e * v). Set λ < 10^-10 m and solve for v. Plugging in the values, v = h / (m_e * λ) = 6.63 x 10^-34 J·s / (9.11 x 10^-31 kg * 10^-10 m) ≈ 7.3 x 10^6 m/s.

Question 16

The uncertainty principle was derived by whom?

Accepted Answer

The uncertainty principle was derived by Werner Heisenberg. It is a fundamental concept in quantum mechanics that states there is a limit to the precision with which certain pairs of physical properties, like position and momentum, can be known simultaneously.

Question 17

What potential difference is needed to accelerate a proton from rest to give it a wavelength of  m?

Accepted Answer

The answer of What potential difference is needed to accelerate...

Question 18

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 also applies to energy and time, indicating that the more precisely one is known, the less precisely the other can be known. This is similar to the position and momentum uncertainty relationship.

Question 19

The de Broglie wavelength of a 0.060-kg golf ball is 3.56 *10^-³⁴m. What is its speed? (h = 6.63 *10^-³⁴ J.s)

Accepted Answer

The de Broglie wavelength formula is λ = h / (mv). Solving for v gives v = h / (mλ). Substituting the given values (h = 6.63 x 10^-34 J·s, m = 0.060 kg, λ = 3.56 x 10^-34 m) results in v ≈ 31 m/s.

Question 20

An electron microscope operates with electrons of kinetic energy 100 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...

Quiz 28: Quantum Theory

If the measured momentum of an electron is 3.20 10^-²⁷ kg.m/s with an uncertainty of 4.8 10^-²⁸kg.m/s, what is the minimum uncertainty in the position? (h = 6.63 * 10^-³⁴ J.s)

What is the energy of a photon that has the same wavelength as a 24 eV electron? (h = 6.63 10^-³⁴ J.s, m_e = 9.1110^-³¹ kg)

That light has a dual nature is referring to light:

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

When stands for Planck's constant, what does (read as "h bar") stand for?

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 (mass = 1.67 10 ^- ²⁷kg) has a kinetic energy of 1.00 MeV. If its momentum is measured with an uncertainty of 2.00%, what is the minimum uncertainty in its position? (h = 6.63 10 ^- ³⁴ J.s and 1 eV = 1.6 *10 ^- ¹⁹ J)

If an electron has a measured wavelength of 1.20 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)

When an electron is in a magnetic field, different spin states associated with the electron's magnetic moment will occur. What are these states called?

Starting from rest, an electron accelerates through a potential difference of 67 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)

When electrons are placed in a magnetic field, their spin orientations are quantized. How many orientations with respect to the field may result?

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

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?

In the STM, what are the S and T?

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 10^-³¹ kg and h = 6.63 10^-³⁴ J.s)

The uncertainty principle was derived by whom?

What potential difference is needed to accelerate a proton from rest to give it a wavelength of m?

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 de Broglie wavelength of a 0.060-kg golf ball is 3.56 10^-³⁴m. What is its speed? (h = 6.63 10^-³⁴ J.s)

An electron microscope operates with electrons of kinetic energy 100 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)

Quiz 28: Quantum Theory

If the measured momentum of an electron is 3.20 *10-27 kg.m/s with an uncertainty of 4.8 *10-28 kg.m/s, what is the minimum uncertainty in the position? (h = 6.63 * 10-34 J.s)

What is the energy of a photon that has the same wavelength as a 24 eV electron? (h = 6.63 *10-34 J.s, me = 9.11*10-31 kg)

That light has a dual nature is referring to light:

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

When stands for Planck's constant, what does (read as "h bar") stand for?

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 (mass = 1.67 *10 - 27 kg) has a kinetic energy of 1.00 MeV. If its momentum is measured with an uncertainty of 2.00%, what is the minimum uncertainty in its position? (h = 6.63 *10 - 34 J.s and 1 eV = 1.6 *10 - 19 J)

If an electron has a measured wavelength of 1.20 *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)

When an electron is in a magnetic field, different spin states associated with the electron's magnetic moment will occur. What are these states called?

Starting from rest, an electron accelerates through a potential difference of 67 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)

When electrons are placed in a magnetic field, their spin orientations are quantized. How many orientations with respect to the field may result?

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

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?

In the STM, what are the S and T?

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 *10-31 kg and h = 6.63 *10-34 J.s)

The uncertainty principle was derived by whom?

What potential difference is needed to accelerate a proton from rest to give it a wavelength of m?

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 de Broglie wavelength of a 0.060-kg golf ball is 3.56 *10-34 m. What is its speed? (h = 6.63 *10-34 J.s)

An electron microscope operates with electrons of kinetic energy 100 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)

If the measured momentum of an electron is 3.20 10^-²⁷ kg.m/s with an uncertainty of 4.8 10^-²⁸kg.m/s, what is the minimum uncertainty in the position? (h = 6.63 * 10^-³⁴ J.s)

What is the energy of a photon that has the same wavelength as a 24 eV electron? (h = 6.63 10^-³⁴ J.s, m_e = 9.1110^-³¹ kg)

A proton (mass = 1.67 10 ^- ²⁷kg) has a kinetic energy of 1.00 MeV. If its momentum is measured with an uncertainty of 2.00%, what is the minimum uncertainty in its position? (h = 6.63 10 ^- ³⁴ J.s and 1 eV = 1.6 *10 ^- ¹⁹ J)

If an electron has a measured wavelength of 1.20 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 67 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)

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 10^-³¹ kg and h = 6.63 10^-³⁴ J.s)

The de Broglie wavelength of a 0.060-kg golf ball is 3.56 10^-³⁴m. What is its speed? (h = 6.63 10^-³⁴ J.s)

An electron microscope operates with electrons of kinetic energy 100 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)