Question 1

The light intensity incident on a metallic surface produces photoelectrons with a maximum kinetic energy of 2 eV.The light intensity is doubled.Determine the maximum kinetic energy of the photoelectrons (in eV).

Accepted Answer

The maximum kinetic energy of the photoelectrons is directly proportional to the frequency (or energy) of the incident light. Doubling the intensity of the light does not directly affect the frequency (or energy) of the photons, so the maximum kinetic energy of the photoelectrons remains the same. Therefore, the answer is B) 2.

Question 2

The experimental observation(s)below that require(s)a quantum explanation for the photoelectric effect

Accepted Answer

The observation that the maximum kinetic energy of the photoelectrons is related linearly to the frequency of light is a key experimental observation that requires a quantum explanation. According to classical physics, increasing the intensity of the light should increase the number of electrons emitted, but not the kinetic energy of the photoelectrons. Only a quantum explanation, using the concept of photons and their energy, can explain why increasing the frequency of light increases the kinetic energy of the photoelectrons.

Question 3

What is the maximum kinetic energy (in eV)of a photoelectron when a surface,whose work function is 5.0 eV,is illuminated by photons whose wavelength is 400 nm?

Accepted Answer

D

Question 4

Your temperature is 98.6$\degree$F.Assuming your skin is a perfect radiator ($\varepsilon$ = 1),determine the wavelength corresponding to the largest intensity (in $\mu$m).

Accepted Answer

The peak wavelength can be calculated using Wien's displacement law: λ_max = b/T, where b is Wien's constant (approximately 2898 μm*K) and T is the temperature in Kelvin. Converting 98.6°F to Kelvin gives approximately 310K, leading to a peak wavelength of about 9.3 μm.

Question 5

A 15-kg mass,attached to a massless spring whose force constant is 2 500 N/m,has an amplitude of 4 cm.Assuming the energy is quantized,find the quantum number of the system,n,if E_n = nhf.

Accepted Answer

The energy of the system is given by:$$E_n = nhf$$where:* $n$ is the quantum number* $h$ is the Planck constant* $f$ is the frequency of the systemThe frequency of the system is given by:$$f = \frac{1}{2\pi}\sqrt{\frac{k}{m}}$$where:* $k$ is the force constant* $m$ is the massSubstituting the given values into the equation for the frequency, we get:$$f = \frac{1}{2\pi}\sqrt{\frac{2500 	ext{ N/m}}{15 	ext{ kg}}} = 2.83 	ext{ Hz}$$Substituting the given values into the equation for the energy, we get:$$E_n = nhf = n(6.626 	imes 10^{-34} 	ext{ J s})(2.83 	ext{ Hz}) = 1.87 	imes 10^{-33} n 	ext{ J}$$The amplitude of the system is given by:$$A = \sqrt{\frac{2E_n}{k}}$$Substituting the given values into the equation for the amplitude, we get:$$A = \sqrt{\frac{2(1.87 	imes 10^{-33} n 	ext{ J})}{2500 	ext{ N/m}}} = 1.13 	imes 10^{-16} \sqrt{n} 	ext{ m}$$The given amplitude is 4 cm, which is equal to $4 	imes 10^{-2} 	ext{ m}$. Setting this equal to the equation for the amplitude, we get:$$4 	imes 10^{-2} 	ext{ m} = 1.13 	imes 10^{-16} \sqrt{n} 	ext{ m}$$Solving for $n$, we get:$$n = \left(\frac{4 	imes 10^{-2} 	ext{ m}}{1.13 	imes 10^{-16} 	ext{ m}}ight)^2 = 1.26 	imes 10^{33}$$Therefore, the quantum number of the system is $n = 1.26 	imes 10^{33}$.

Question 6

What is the maximum velocity (in km/s)of a photoelectron emitted from a surface whose work function is 5.0 eV when illuminated by a light whose wavelength is 200 nm?

Accepted Answer

We can use the equation:

Kmax = hv - φ

Where:

Kmax = maximum kinetic energy of the photoelectron 
h = Planck's constant 
v = frequency of the light (c/λ, where c is the speed of light and λ is the wavelength) 
φ = work function

First, we need to find the frequency of the light:

v = c/λ = (3.00 x 10^8 m/s) / (200 x 10^-9 m) = 1.50 x 10^15 Hz

Next, we need to convert the work function to joules:

φ = 5.0 eV x 1.60 x 10^-19 J/eV = 8.0 x 10^-19 J

Now we can substitute these values into the equation:

Kmax = hv - φ = (6.63 x 10^-34 J s)(1.50 x 10^15 Hz) - 8.0 x 10^-19 J = 6.59 x 10^-19 J

Finally, we can convert the kinetic energy to velocity:

Kmax = 1/2 mv^2

v = sqrt(2Kmax/m) = sqrt(2(6.59 x 10^-19 J)/(9.11 x 10^-31 kg)) = 652 km/s

Therefore, the maximum velocity of the photoelectron is approximately 652 km/s. The correct answer is choice B.

Question 7

Assume electrons are accelerated through a potential difference of 25 000 V inside a TV picture tube.What is the minimum wavelength that could be produced when the electrons strike the phosphor? (1 Å = 10 ^- ¹⁰ m)

Accepted Answer

The minimum wavelength is given by the de Broglie wavelength equation:$$\lambda = \frac{h}{p}$$where h is Planck's constant and p is the momentum of the electron. The momentum of the electron is given by:$$p = \sqrt{2mK}$$where m is the mass of the electron and K is the kinetic energy of the electron. The kinetic energy of the electron is given by:$$K = eV$$where e is the charge of the electron and V is the potential difference through which the electron is accelerated. Substituting these equations into the de Broglie wavelength equation, we get:$$\lambda = \frac{h}{\sqrt{2meV}}$$Plugging in the values for h, m, e, and V, we get:$$\lambda = \frac{6.626 	imes 10^{-34} 	ext{ J s}}{\sqrt{2(9.109 	imes 10^{-31} 	ext{ kg})(1.602 	imes 10^{-19} 	ext{ C})(25000 	ext{ V})}}$$$$\lambda = 0.50 	imes 10^{-10} 	ext{ m} = 0.50 	ext{ Å}$$Therefore, the minimum wavelength that could be produced when the electrons strike the phosphor is 0.50 Å.

Question 8

In an experiment different wavelengths of light,all able to eject photoelectrons,shine on a freshly prepared (oxide-free)zinc surface.Which statement is true?

Accepted Answer

The answer of In an experiment different wavelengths of light,all...

Question 9

How much energy is in an 89.7 MHz photon of FM-radiation?

Accepted Answer

The energy of a photon can be calculated using the equation E = hf, where h is the Planck's constant (6.626 × 10^-34 J*s) and f is the frequency of the radiation. 
E = hf = (6.626 × 10^-34 J*s) × (89.7 × 10^6 Hz) = 5.93 × 10^-20 J
Rounding to two significant figures, the answer is 5.9 × 10^-20 J, which corresponds to choice D.

Question 10

How much energy is in a 63 kHz photon of AM-radiation?

Accepted Answer

The energy of a photon can be calculated using the formula E = hf, where E is the energy in joules, h is Planck's constant (6.626 x 10^-34 J/s), and f is the frequency in hertz. 
Substituting the given values, we get:
E = (6.626 x 10^-34 J/s) x (63 x 10^3 Hz) 
E = 4.175 x 10^-28 J 
Rounding off to two significant figures, we get:
E = 4.2 x 10^-28 J 
Therefore, the best choice is C.

Question 11

A stopping potential of 3.2 V is needed for radiation whose wavelength is 200 nm.What is the work function (in eV)of the material?

Accepted Answer

The answer of A stopping potential of 3.2 V is...

Question 12

The threshold wavelength for photoelectric emission of a particular substance is 500 nm.What is the work function (in eV)?

Accepted Answer

The work function (Φ) is calculated using the formula Φ = hc/λ, where h is Planck's constant (4.1357 x 10^-15 eV·s), c is the speed of light (3 x 10^8 m/s), and λ is the threshold wavelength (500 nm = 500 x 10^-9 m). Substituting these values gives Φ ≈ 2.5 eV.

Question 13

What is the maximum kinetic energy (in eV)of a photoelectron emitted from a surface whose work function is 5.0 eV when illuminated by a light whose wavelength is 200 nm?

Accepted Answer

The answer of What is the maximum kinetic energy (in...

Question 14

The number of photons per second passing a plane perpendicular to a collimated monochromatic (one frequency)beam of light transporting power P is directly proportional to

Accepted Answer

The number of photons in a beam of light is directly proportional to the power of the beam (P), as each photon carries a certain amount of energy. However, the number of photons is also inversely proportional to the energy of each photon, which is proportional to the frequency (E = hf) and inversely proportional to the wavelength (E = hc/λ). Therefore, the number of photons is directly proportional to P/λ, or equivalently to P and inversely proportional to λ. Therefore, the best choice is (a) and (c): wavelength and power.

Question 15

A solid state pulsed laser has an energy of 400 mJ per pulse.If its wavelength is 1.06 *10 ^- ⁶ m,how many photons are in each pulse?

Accepted Answer

The answer of A solid state pulsed laser has an...

Question 16

A pendulum located where $g = 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } }$ has a 0.500 kg bob and a 4.00 Hz oscillation frequency.If it is released from a point 0.150 m above the lowest point it reaches,the number of quanta in this oscillation is

Accepted Answer

The energy of the pendulum is:$$E = \frac{1}{2}mv^2 + mgh = \frac{1}{2}m\omega^2A^2 + mgA(1-\cos\theta)$$where $m$ is the mass of the bob, $v$ is the velocity of the bob, $\omega$ is the angular frequency, $A$ is the amplitude, $g$ is the acceleration due to gravity, $h$ is the height of the bob above the lowest point, and $\theta$ is the angle of the pendulum from the vertical.At the lowest point, $\theta = 0$ and $v = \omega A$, so the energy is:$$E = \frac{1}{2}m\omega^2A^2 + mgA$$At the highest point, $\theta = \pi$ and $v = 0$, so the energy is:$$E = mgA(1-\cos\pi) = 2mgA$$The number of quanta in the oscillation is:$$n = \frac{E}{hf}$$where $h$ is the Planck constant and $f$ is the frequency.Substituting the given values, we get:$$n = \frac{\frac{1}{2}m\omega^2A^2 + mgA}{hf} = \frac{\frac{1}{2}(0.500 \text{ kg})(2\pi \times 4.00 \text{ Hz})^2(0.150 \text{ m})^2 + (0.500 \text{ kg})(9.80 \text{ m/s}^2)(0.150 \text{ m})}{(6.626 \times 10^{-34} \text{ J s})(4.00 \text{ Hz})} = 1.11 \times 10^{33}$$Therefore, the correct answer is B.

Question 17

Photoelectrons are ejected when monochromatic light shines on a freshly-prepared (oxide-free)sodium surface.In order to obtain the maximum increase in the number of electrons ejected per second,the experimenter needs to

Accepted Answer

Increasing the intensity of the light increases the number of photons hitting the surface per second, which directly increases the number of electrons ejected per second. Increasing the area illuminated also increases the number of electrons ejected by providing more surface area for the light to interact with. Changing the frequency (option A) affects the energy of the ejected electrons but not the number of electrons ejected per second.

Question 18

A helium-neon laser emits red light having a wavelength of 6.4 *10 ^- ⁷ m and a power of 0.5 mW.How many photons are emitted each second?

Accepted Answer

The answer of A helium-neon laser emits red light having...

Question 19

A photon whose energy is 8.00 *10 ^- ¹⁵ J is scattered off an electron at a 90$\degree$ angle.What is the wavelength of the scattered wave?

Accepted Answer

The correct answer is A because the wavelength of the scattered wave is given by the Compton wavelength divided by the sine of the scattering angle. The Compton wavelength is 2.4263102389(81)×10^-12 m, and the scattering angle is 90 degrees, so the wavelength of the scattered wave is 2.4263102389(81)×10^-12 m / sin(90 degrees) = 2.731599190(91)×10^-11 m.

Question 20

The light intensity incident on a metallic surface with a work function of 3 eV produces photoelectrons with a maximum kinetic energy of 2 eV.The frequency of the light is doubled.Determine the maximum kinetic energy (in eV).

Accepted Answer

When the frequency of the light is doubled, the energy of the photons is also doubled. Initially, the photon energy is 5 eV (3 eV work function + 2 eV kinetic energy). Doubling the frequency doubles the photon energy to 10 eV. Subtracting the work function (3 eV) from this gives a maximum kinetic energy of 7 eV.

Quiz 28: Quantum Physics

The light intensity incident on a metallic surface produces photoelectrons with a maximum kinetic energy of 2 eV.The light intensity is doubled.Determine the maximum kinetic energy of the photoelectrons (in eV) .

The experimental observation(s) below that require(s) a quantum explanation for the photoelectric effect

What is the maximum kinetic energy (in eV) of a photoelectron when a surface,whose work function is 5.0 eV,is illuminated by photons whose wavelength is 400 nm?

Your temperature is 98.6 $\degree$ F.Assuming your skin is a perfect radiator ( $\varepsilon$ = 1) ,determine the wavelength corresponding to the largest intensity (in $\mu$ m) .

A 15-kg mass,attached to a massless spring whose force constant is 2 500 N/m,has an amplitude of 4 cm.Assuming the energy is quantized,find the quantum number of the system,n,if E_n = nhf.

What is the maximum velocity (in km/s) of a photoelectron emitted from a surface whose work function is 5.0 eV when illuminated by a light whose wavelength is 200 nm?

Assume electrons are accelerated through a potential difference of 25 000 V inside a TV picture tube.What is the minimum wavelength that could be produced when the electrons strike the phosphor? (1 Å = 10 ^- ¹⁰ m)

In an experiment different wavelengths of light,all able to eject photoelectrons,shine on a freshly prepared (oxide-free) zinc surface.Which statement is true?

How much energy is in an 89.7 MHz photon of FM-radiation?

How much energy is in a 63 kHz photon of AM-radiation?

A stopping potential of 3.2 V is needed for radiation whose wavelength is 200 nm.What is the work function (in eV) of the material?

The threshold wavelength for photoelectric emission of a particular substance is 500 nm.What is the work function (in eV) ?

What is the maximum kinetic energy (in eV) of a photoelectron emitted from a surface whose work function is 5.0 eV when illuminated by a light whose wavelength is 200 nm?

The number of photons per second passing a plane perpendicular to a collimated monochromatic (one frequency) beam of light transporting power P is directly proportional to

A solid state pulsed laser has an energy of 400 mJ per pulse.If its wavelength is 1.06 *10 ^- ⁶ m,how many photons are in each pulse?

A pendulum located where $g = 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } }$ has a 0.500 kg bob and a 4.00 Hz oscillation frequency.If it is released from a point 0.150 m above the lowest point it reaches,the number of quanta in this oscillation is

Photoelectrons are ejected when monochromatic light shines on a freshly-prepared (oxide-free) sodium surface.In order to obtain the maximum increase in the number of electrons ejected per second,the experimenter needs to

A helium-neon laser emits red light having a wavelength of 6.4 *10 ^- ⁷ m and a power of 0.5 mW.How many photons are emitted each second?

A photon whose energy is 8.00 *10 ^- ¹⁵ J is scattered off an electron at a 90 $\degree$ angle.What is the wavelength of the scattered wave?

The light intensity incident on a metallic surface with a work function of 3 eV produces photoelectrons with a maximum kinetic energy of 2 eV.The frequency of the light is doubled.Determine the maximum kinetic energy (in eV) .

Quiz 28: Quantum Physics

The light intensity incident on a metallic surface produces photoelectrons with a maximum kinetic energy of 2 eV.The light intensity is doubled.Determine the maximum kinetic energy of the photoelectrons (in eV) .

The experimental observation(s) below that require(s) a quantum explanation for the photoelectric effect

What is the maximum kinetic energy (in eV) of a photoelectron when a surface,whose work function is 5.0 eV,is illuminated by photons whose wavelength is 400 nm?

Your temperature is 98.6 °\degree° F.Assuming your skin is a perfect radiator ( ε\varepsilonε = 1) ,determine the wavelength corresponding to the largest intensity (in μ\muμ m) .

A 15-kg mass,attached to a massless spring whose force constant is 2 500 N/m,has an amplitude of 4 cm.Assuming the energy is quantized,find the quantum number of the system,n,if En = nhf.

What is the maximum velocity (in km/s) of a photoelectron emitted from a surface whose work function is 5.0 eV when illuminated by a light whose wavelength is 200 nm?

Assume electrons are accelerated through a potential difference of 25 000 V inside a TV picture tube.What is the minimum wavelength that could be produced when the electrons strike the phosphor? (1 Å = 10 - 10 m)

In an experiment different wavelengths of light,all able to eject photoelectrons,shine on a freshly prepared (oxide-free) zinc surface.Which statement is true?

How much energy is in an 89.7 MHz photon of FM-radiation?

How much energy is in a 63 kHz photon of AM-radiation?

A stopping potential of 3.2 V is needed for radiation whose wavelength is 200 nm.What is the work function (in eV) of the material?

The threshold wavelength for photoelectric emission of a particular substance is 500 nm.What is the work function (in eV) ?

What is the maximum kinetic energy (in eV) of a photoelectron emitted from a surface whose work function is 5.0 eV when illuminated by a light whose wavelength is 200 nm?

The number of photons per second passing a plane perpendicular to a collimated monochromatic (one frequency) beam of light transporting power P is directly proportional to

A solid state pulsed laser has an energy of 400 mJ per pulse.If its wavelength is 1.06 *10 - 6 m,how many photons are in each pulse?

A pendulum located where g=9.80ms2g = 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } }g=9.80s2m​ has a 0.500 kg bob and a 4.00 Hz oscillation frequency.If it is released from a point 0.150 m above the lowest point it reaches,the number of quanta in this oscillation is

Photoelectrons are ejected when monochromatic light shines on a freshly-prepared (oxide-free) sodium surface.In order to obtain the maximum increase in the number of electrons ejected per second,the experimenter needs to

A helium-neon laser emits red light having a wavelength of 6.4 *10 - 7 m and a power of 0.5 mW.How many photons are emitted each second?

A photon whose energy is 8.00 *10 - 15 J is scattered off an electron at a 90 °\degree° angle.What is the wavelength of the scattered wave?

The light intensity incident on a metallic surface with a work function of 3 eV produces photoelectrons with a maximum kinetic energy of 2 eV.The frequency of the light is doubled.Determine the maximum kinetic energy (in eV) .

Your temperature is 98.6 $\degree$ F.Assuming your skin is a perfect radiator ( $\varepsilon$ = 1) ,determine the wavelength corresponding to the largest intensity (in $\mu$ m) .

A 15-kg mass,attached to a massless spring whose force constant is 2 500 N/m,has an amplitude of 4 cm.Assuming the energy is quantized,find the quantum number of the system,n,if E_n = nhf.

Assume electrons are accelerated through a potential difference of 25 000 V inside a TV picture tube.What is the minimum wavelength that could be produced when the electrons strike the phosphor? (1 Å = 10 ^- ¹⁰ m)

A solid state pulsed laser has an energy of 400 mJ per pulse.If its wavelength is 1.06 *10 ^- ⁶ m,how many photons are in each pulse?

A pendulum located where $g = 9.80 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } }$ has a 0.500 kg bob and a 4.00 Hz oscillation frequency.If it is released from a point 0.150 m above the lowest point it reaches,the number of quanta in this oscillation is

A helium-neon laser emits red light having a wavelength of 6.4 *10 ^- ⁷ m and a power of 0.5 mW.How many photons are emitted each second?

A photon whose energy is 8.00 *10 ^- ¹⁵ J is scattered off an electron at a 90 $\degree$ angle.What is the wavelength of the scattered wave?