Question 1

What is the maximum velocity of a photoelectron emitted from a surface with work function 5.22 eV when illuminated by 200-nm ultraviolet light? (m_electron = 9.11 × 10−³¹ kg,h = 6.63 × 10−³⁴ J⋅s,1 eV = 1.60 × 10−¹⁹ J,and 1 nm = 10−⁹ m)

Accepted Answer

The maximum kinetic energy of the photoelectron is given by:$$KE_{max} = h
u - \phi$$where:* $$h$$ is Planck's constant* $$
u$$ is the frequency of the light* $$\phi$$ is the work functionThe frequency of the light is given by:$$
u = \frac{c}{\lambda}$$where:* $$c$$ is the speed of light* $$\lambda$$ is the wavelength of the lightSubstituting the given values into the equations, we get:$$KE_{max} = (6.63 	imes 10^{-34} J \cdot s)(3 	imes 10^8 m/s)/(200 	imes 10^{-9} m) - 5.22 eV$$$$KE_{max} = 9.94 	imes 10^{-19} J$$The maximum velocity of the photoelectron is given by:$$v = \sqrt{\frac{2KE_{max}}{m_e}}$$where:* $$m_e$$ is the mass of the electronSubstituting the given values into the equation, we get:$$v = \sqrt{\frac{2(9.94 	imes 10^{-19} J)}{9.11 	imes 10^{-31} kg}} = 5.91 	imes 10^5 m/s$$Therefore, the maximum velocity of the photoelectron is 591,000 m/s.

Question 2

Of the following energies for photons,which is the least energy that could result in photoelectron production if the work function is 1.60 eV?

Accepted Answer

The energy of the photon must be equal to or greater than the work function to produce photoelectrons. 2.90 eV is the least energy greater than 1.60 eV.

Question 3

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 de Broglie wavelength of an electron is given by:
λ = h/p
where p is the momentum of the electron. We can find the momentum by using the equation:
p = √(2mKE)
where m is the mass of the electron, KE is its kinetic energy, and we know that the electron was accelerated through a potential difference of 67 V.

First, we need to convert the potential difference into kinetic energy:
KE = eV
where e is the charge on the electron. Substituting the given values, we get:
KE = (1.60 × 10^-19 C)(67 V) = 1.07 × 10^-17 J

Next, we can find the momentum:
p = √(2mKE) = √(2(9.11 × 10^-31 kg)(1.07 × 10^-17 J)) = 3.29 × 10^-24 kg m/s

Finally, we can find the de Broglie wavelength:
λ = h/p = (6.63 × 10^-34 J s)/(3.29 × 10^-24 kg m/s) = 2.02 × 10^-10 m
which is approximately equal to 1.5 × 10^-10 m, or choice B.

Question 4

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 5

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...

Question 6

What potential difference is needed to accelerate a proton from rest to give it a wavelength of 2.00 × 10^-12 m?

Accepted Answer

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

Question 7

How much energy (in eV)does a photon of 500-nm light have? (h = 6.63 × 10−³⁴ J⋅s,c = 3.00 × 10⁸ m/s,1 eV = 1.60 × 10−¹⁹ J,and 1 nm = 10−⁹ m)

Accepted Answer

The energy of a photon (E) can be calculated using the equation:

E = hc/λ

where h is Planck's constant, c is the speed of light, and λ is the wavelength of the photon.

Plugging in the given values:

E = (6.63 x 10^-34 J s)(3.00 x 10^8 m/s)/(500 x 10^-9 m)

E = 3.98 x 10^-19 J

Converting to eV:

E(eV) = (3.98 x 10^-19 J)/(1.60 x 10^-19 J/eV)

E(eV) = 2.48 eV

Therefore, the answer is B.

Question 8

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)

Accepted Answer

The uncertainty in momentum Δp is 2% of the proton's momentum. Using the kinetic energy, we can find the velocity and thus the momentum. Then, using Heisenberg's uncertainty principle ΔxΔp ≥ h/4π, we can calculate the minimum uncertainty in position Δx.

Question 9

According to de Broglie,as the momentum of a moving particle is quartered,the corresponding wavelength changes by what factor?

Accepted Answer

According to de Broglie's equation, λ = h/p, where λ is wavelength, h is Planck's constant, and p is momentum. As momentum (p) is inversely proportional to wavelength (λ), if momentum is quartered (divided by 4), then wavelength will be quadrupled (multiplied by 4). Therefore, the corresponding wavelength changes by a factor of 4. The answer is D.

Question 10

Sources of red,blue,and yellow light each emit light with a power of 50 mW.Which source emits the least photons per second?

Accepted Answer

The number of photons emitted per second is directly proportional to the power of the source. Since all three sources emit at the same power of 50 mW, the source with the highest frequency (blue) will have the least number of photons per second because it has a higher energy per photon. Therefore, the blue source emits the least photons per second.

Question 11

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)

Accepted Answer

The uncertainty principle states that the uncertainty in position (Δx) and the uncertainty in momentum (Δp) are related by the inequality ΔxΔp ≥ h/4π. Rearranging this equation to solve for Δx gives Δx ≥ h/4πΔp. Plugging in the values from the problem, we get Δx ≥ (6.63 × 10^-34 J·s)/(4π(4.8 × 10^-27 kg·m/s)) ≈ 1.1 × 10^-17 m, which is closest to choice D.

Question 12

What is the de Broglie wavelength for a proton (m = 1.67 × 10−²⁷ kg)moving at a speed of 3.0 × 10⁶ m/s? (h = 6.63 × 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 × 10^−34 J⋅s / (1.67 × 10^−27 kg × 3.0 × 10^6 m/s) = 1.3 × 10^−13 m.

Question 13

A detector absorbs 1.0 × 10⁹ photons of monochromatic light and their total energy is found to be 0.33 nJ.What is the wavelength associated with these photons? (h = 6.63 × 10−³⁴ J⋅s,c = 3.00 × 10⁸ m/s)

Accepted Answer

The energy of a single photon is given by E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength. The total energy of the photons is given, so first, we find the energy of a single photon by dividing the total energy by the number of photons. Then, we rearrange the formula to solve for λ.Total energy = 0.33 nJ = 0.33 × 10^-9 JNumber of photons = 1.0 × 10^19Energy per photon = (0.33 × 10^-9 J) / (1.0 × 10^19) = 3.3 × 10^-28 JUsing E = hc/λ, we solve for λ:λ = hc/E  = (6.63 × 10^-34 J⋅s)(3.00 × 10^8 m/s) / (3.3 × 10^-28 J)  = 6.03 × 10^-7 m  = 600 nm

Question 14

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

Accepted Answer

The de Broglie wavelength is inversely proportional to momentum. Since the proton is much more massive than the electron, for the same wavelength, the proton must have a lower speed. Kinetic energy depends on both mass and speed, and since the proton has a much larger mass, it will have a lower kinetic energy for the same wavelength.

Question 15

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 de Broglie wavelength formula λ = h/p can be used to find the momentum p, and then the kinetic energy KE = p²/(2m) can be calculated. Converting the result to eV gives approximately 105 eV.

Question 16

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: v = (6.63 × 10^-34 J⋅s) / (0.060 kg × 3.56 × 10^-34 m) = 31 m/s.

Question 17

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 18

The microwave in the kitchen has a label that indicates it produces its microwaves at a frequency of 2450 MHz.What is the energy associated with one of these microwave photons? (h = 6.63 × 10−³⁴ J⋅s)

Accepted Answer

The answer of The microwave in the kitchen has a...

Quiz 28: Atomic Physics: Part A

What is the maximum velocity of a photoelectron emitted from a surface with work function 5.22 eV when illuminated by 200-nm ultraviolet light? (m_electron = 9.11 × 10−³¹ kg,h = 6.63 × 10−³⁴ J⋅s,1 eV = 1.60 × 10−¹⁹ J,and 1 nm = 10−⁹ m)

Of the following energies for photons,which is the least energy that could result in photoelectron production if the work function is 1.60 eV?

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)

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?

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)

What potential difference is needed to accelerate a proton from rest to give it a wavelength of 2.00 × 10^-12 m?

How much energy (in eV) does a photon of 500-nm light have? (h = 6.63 × 10−³⁴ J⋅s,c = 3.00 × 10⁸ m/s,1 eV = 1.60 × 10−¹⁹ J,and 1 nm = 10−⁹ m)

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)

According to de Broglie,as the momentum of a moving particle is quartered,the corresponding wavelength changes by what factor?

Sources of red,blue,and yellow light each emit light with a power of 50 mW.Which source emits the least photons per second?

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 de Broglie wavelength for a proton (m = 1.67 × 10−²⁷ kg) moving at a speed of 3.0 × 10⁶ m/s? (h = 6.63 × 10−³⁴ J⋅s)

A detector absorbs 1.0 × 10⁹ photons of monochromatic light and their total energy is found to be 0.33 nJ.What is the wavelength associated with these photons? (h = 6.63 × 10−³⁴ J⋅s,c = 3.00 × 10⁸ m/s)

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

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)

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)

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)

The microwave in the kitchen has a label that indicates it produces its microwaves at a frequency of 2450 MHz.What is the energy associated with one of these microwave photons? (h = 6.63 × 10−³⁴ J⋅s)

Quiz 28: Atomic Physics: Part A

What is the maximum velocity of a photoelectron emitted from a surface with work function 5.22 eV when illuminated by 200-nm ultraviolet light? (melectron = 9.11 × 10−31 kg,h = 6.63 × 10−34 J⋅s,1 eV = 1.60 × 10−19 J,and 1 nm = 10−9 m)

Of the following energies for photons,which is the least energy that could result in photoelectron production if the work function is 1.60 eV?

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)

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?

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)

What potential difference is needed to accelerate a proton from rest to give it a wavelength of 2.00 × 10-12 m?

How much energy (in eV) does a photon of 500-nm light have? (h = 6.63 × 10−34 J⋅s,c = 3.00 × 108 m/s,1 eV = 1.60 × 10−19 J,and 1 nm = 10−9 m)

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)

According to de Broglie,as the momentum of a moving particle is quartered,the corresponding wavelength changes by what factor?

Sources of red,blue,and yellow light each emit light with a power of 50 mW.Which source emits the least photons per second?

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 de Broglie wavelength for a proton (m = 1.67 × 10−27 kg) moving at a speed of 3.0 × 106 m/s? (h = 6.63 × 10−34 J⋅s)

A detector absorbs 1.0 × 109 photons of monochromatic light and their total energy is found to be 0.33 nJ.What is the wavelength associated with these photons? (h = 6.63 × 10−34 J⋅s,c = 3.00 × 108 m/s)

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

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)

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)

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)

The microwave in the kitchen has a label that indicates it produces its microwaves at a frequency of 2450 MHz.What is the energy associated with one of these microwave photons? (h = 6.63 × 10−34 J⋅s)

What is the maximum velocity of a photoelectron emitted from a surface with work function 5.22 eV when illuminated by 200-nm ultraviolet light? (m_electron = 9.11 × 10−³¹ kg,h = 6.63 × 10−³⁴ J⋅s,1 eV = 1.60 × 10−¹⁹ J,and 1 nm = 10−⁹ m)

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)

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)

What potential difference is needed to accelerate a proton from rest to give it a wavelength of 2.00 × 10^-12 m?

How much energy (in eV) does a photon of 500-nm light have? (h = 6.63 × 10−³⁴ J⋅s,c = 3.00 × 10⁸ m/s,1 eV = 1.60 × 10−¹⁹ J,and 1 nm = 10−⁹ m)

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 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 de Broglie wavelength for a proton (m = 1.67 × 10−²⁷ kg) moving at a speed of 3.0 × 10⁶ m/s? (h = 6.63 × 10−³⁴ J⋅s)

A detector absorbs 1.0 × 10⁹ photons of monochromatic light and their total energy is found to be 0.33 nJ.What is the wavelength associated with these photons? (h = 6.63 × 10−³⁴ J⋅s,c = 3.00 × 10⁸ m/s)

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)

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)

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)

The microwave in the kitchen has a label that indicates it produces its microwaves at a frequency of 2450 MHz.What is the energy associated with one of these microwave photons? (h = 6.63 × 10−³⁴ J⋅s)