Photons: Energy, Momentum & Radiation Pressure

The number of photons per second emitted by the source of monochromatic light of wavelength $600$ nm, when it delivers the power of $3.3 \times 10^{-3}$ W will be

(Planck's constant $= 6.6 \times 10^{-34}$ Js, $c = 3 \times 10^{8}$ m/s)

Number of photons of equal energy emitted per second by a 6 mW laser source operating at 663 nm is ________.

(Given: $h = 6.63 \times 10^{-34}$ J.s and $c = 3 \times 10^{8}$ m/s)

Match List I with List II.

A monochromatic source of light operating at 15 kW emits $2.5 \times 10^{22}$ photons $/\text{s}$. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to ______. (Take $h = 6.6 \times 10^{-34}\text{ J.s}$ and $c = 3 \times 10^{8}\text{ m/s}$ ).

A parallel beam of light is incident normally on a plane surface absorbing $40\%$ of light and reflecting the rest. If the incident beam carries $60$ W of power the force exerted by it on the surface is (C = velocity of light = $3 \times 10^{8}$ m/s)

Which of the following phenomena cannot be explained by wave theory of light?

The ratio of the power of a light source $S_1$ to that of the light source $S_2$ is $2.\ S_1$ is emitting $2 \times 10^{15}$ photons per second at 600 nm. If the wavelength of the source $S_2$ is 300 nm, then the number of photons per second emitted by $S_2$ is __________ $\times 10^{14}$.

A parallel beam of light is incident normally on a plane surface absorbing $50\%$ of the light and reflecting the rest. If the incident beam carries 90 W of power, the force exerted by it on the surface is ( $C =$ velocity of light in air $= 3 \times 10^{8}\text{ m/s}$)

The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed at 2 m away from it, is

A small mirror of mass $m$ is suspended by a massless thread of length $l$. Then the small angle through which the thread will be deflected when a short pulse of laser of energy E falls normal on the mirror

($c =$ speed of light in vacuum and $g =$ acceleration due to gravity)

If $c$ is the velocity of light in free space, the correct statements about photon among the following are:

A. The energy of a photon is $E = h\nu$.

B. The velocity of a photon is $c$.

C. The momentum of a photon, $p = \frac{h\nu}{c}$.

D. In a photon-electron collision, both total energy and total momentum are conserved. E. Photon possesses positive charge.

Choose the correct answer from the options given below:

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason R.

Assertion A: Number of photons increases with increase in frequency of light.

Reason R: Maximum kinetic energy of emitted electrons increases with the frequency of incident radiation.

In the light of the above statements, choose the most appropriate answer from the options given below:

Monochromatic light of frequency $6 \times 10^{14}\text{ Hz}$ is produced by a laser. The power emitted is $2 \times 10^{-3}\text{ W}$.

How many photons per second on an average, are emitted by the source?

(Given $h = 6.63 \times 10^{-34}\text{ Js}$)

Two sources of light emit with a power of $200\text{ W}$. The ratio of number of photons of visible light emitted by each source having wavelengths $300\text{ nm}$ and $500\text{ nm}$ respectively, will be:

If the total energy transferred to a surface in time $t$ is $6.48 \times 10^{5}\text{ J}$, then the magnitude of the total momentum delivered to this surface for complete absorption will be:

Which of the following phenomena is not explained by wave nature of light?

A. reflection

B. diffraction

C. photoelectric effect

D. interference

E. polarization

Choose the most appropriate answer from the options given below:

A small object at rest, absorbs a light pulse of power $20\text{ mW}$ and duration $300\text{ ns}$. Assuming speed of light as $3 \times 10^{8}\text{ m/s}$, the momentum of the object becomes equal to:

Dual nature of light is exhibited by

If a source of electromagnetic radiation having power $15\text{ kW}$ produces $10^{16}$ photons per second, the radiation belongs to a part of spectrum is.

(Take Planck constant $h = 6 \times 10^{-34}\text{ Js}$)

A source of monochromatic light liberates 9 $\times$ 1020 photon per second with wavelength 600 nm when operated at 400 W. The number of photons emitted per second with wavelength of 800 nm by the source of monochromatic light operating at same power will be:

A parallel beam of light of wavelength $900\text{ nm}$ and intensity $100\text{ Wm}^{-2}$ is incident on a surface perpendicular to the beam. The number of photons crossing $1\text{ cm}^{2}$ area perpendicular to the beam in one second is:

A photon has wavelength $3\text{ nm}$, then its momentum and energy respectively will be $[h = 6.63 \times 10^{-34}\text{ Js}, c =$ velocity of light $= 3 \times 10^{8}\text{ m/s}]$

When a photon enters glass from air, which one of the following quantity does not change?

Given below are two statements:

Statement I: Two photons having equal linear momenta have equal wavelengths. Statement II: If the wavelength of photon is decreased, then the momentum and energy of a photon will also decrease.

In the light of the above statements, choose the correct answer from the options given below.

When light of wavelength '$\lambda$' is incident on a photosensitive surface, photons of power 'P' are emitted. The number of photon 'n' emitted in time 't' is [h = Planck's constant, c = velocity of light in vacuum]

The number of photons per second on an average emitted by the source of monochromatic light of wavelength 600nm, when it delivers the power of 3.3 $\times$ 10$-$3 watt will be: (h = 6.6 $\times$ 10$-$34 Js)

The wavelength of an X-ray beam is 10$\mathring{A}$. The mass of a fictitious particle having the same energy as that of the X-ray photons is $\frac{x}{3}h$ kg. The value of x is __________. (h = Planck's constant)

Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respectively. Both the sources emit light of the same power 200 W. The ratio of the number density of photons of X-rays to the number density of photons of the visible light of the given wavelengths is:

Light with an average flux of 20 W/cm2 falls on a non-reflecting surface at normal incidence having surface area 20 cm2. The energy received by the surface during time span of 1 minute is:

A 2 mW laser operates at wavelength of 500 nm. The number of photons that will be emitted per second is: [Given Planck's constant h = 6.6 × 10–34 Js, speed of light c = 3.0 × 108 m/s]

A Laser light of wavelength 660 nm is used to weld Retina detachment. If a Laser pulse of width 60 ms and power 0.5 kW is used the approximate number of photons in the pulse are: [Take Planck's constant h $=$ 6.62 $\times$ 10$-$34 Js]

A 200 W sodium street lamp emits yellow light of wavelength 0.6 $\mu$m. Assuming it to be 25% efficient in converting electrical energy to light, the number of photons of yellow light it emits per second is

A source S1 is producing, 1015 photons per second of wavelength 5000 $\mathring{A}$. Another source S2 is producing 1.02 $\times$ 1015 photons per second of wavelength 5100 $\mathring{A}$. Then, (power of S2)/(power of S1) is equal to

If a source of power $4\text{ kW}$ produces $10^{20}$ photons/second, the radiation belongs to a part of the spectrum called

Monochromatic light of wavelength 667 nm is produced by a helium neon laser. The power emitted is 9 mW. The number of photons arriving per sec. on the average at a target irradiated by this beam is

Photon of frequency $\nu$ has a momentum associated with it. If $c$ is the velocity of light, the momentum is

Monochromatic light of frequency 6.0 $\times$ 1014 Hz is produced by a laser. The power emitted is 2 $\times$ 10$-$3 W. The number of photons emitted, on the average, by the source per second is

The momentum of a photon of energy 1 MeV in kg m/s will be

The value of Planck's constant is

Which one among the following shows particle nature of light?

By photoelectric effect, Einstein proved

The energy of a photon of light is $3\text{ eV}$. Then the wavelength of photon must be

If a photon has velocity $c$ and frequency $\nu$, then which of the following represents its wavelength?

The velocity of photons is proportional to (where $\nu$ = frequency)

Momentum of photon wavelength $\lambda$ is

The wavelength of a 1 keV photon is $1.24 \times 10^{-9}$ m. What is the frequency of 1 MeV photon?

The momentum of a photon of an electromagnetic radiation is $3.3 \times 10^{-29}\text{ kg ms}^{-1}$. What is the frequency of the associated waves?

[$h = 6.6 \times 10^{-34}\text{ Js}$; $c = 3 \times 10^{8}\text{ ms}^{-1}$]

A radio transmitter operates at a frequency 880 kHz and a power of 10 kW. The number of photons emitted per second is

The energy of a photon of wavelength $\lambda$ is