English
NEET (UG)
MCQ Online Mock Tests43
Concept Notes1296
Syllabus

Particle Nature of Light: The Photon

Advertisements

Topics

Estimated time: 10 minutes
CBSE: Class 12

Definition: Photons

The photoelectric effect demonstrates that light behaves as if it consists of energy packets called quanta or photons.

CBSE: Class 12

Formula: Photons

E = hν

where:

  • E = energy of one photon
  • h = Planck’s constant = 6.626 × 10-34 J s
  • ν = frequency of radiation
CBSE: Class 12

Key Properties of Photons

  • A photon has energy equal to hν.
  • A photon moves with the speed of light in vacuum, that is, c.
  • Photons are electrically neutral, so they are not deflected by electric or magnetic fields.
  • All photons of the same frequency have the same energy.
  • Increasing intensity increases the number of photons, not the energy of each photon.

Momentum of a Photon

A photon also carries momentum:

p = \[\frac {E}{c}\] = \[\frac {hν}{c}\] = \[\frac {h}{λ}\]

where:

  • p = momentum of the photon
  • λ = wavelength of radiation
CBSE: Class 12

Importance of Photon

The photon model is important because it explains the photoelectric effect, where electrons are emitted from a metal surface when light of suitable frequency falls on it.

Cause-and-Effect Logic

  • Each photon interacts with one electron.
  • If photon energy is less than the work function, no electron is emitted.
  • If the photon energy is greater than the work function, the electron is emitted with kinetic energy.

Photoelectric Equation

Kmax = hν − ϕ

where:

  • Kmax​ = maximum kinetic energy of emitted electron
  • ϕ = work function of the metal
CBSE: Class 12

Example 1

  • The laser emits monochromatic light of frequency 6.0 × 1014 Hz with power 2.0 × 10−3 W.
  • Part (a) finds the energy of one photon using E = hν, giving E = 3.98 × 10−19 J.
  • Part (b) finds the number of photons per second using P = NE ⇒ N = P/E, giving N ≈ 5.0 × 1015 photons per second.

So this example shows that, given the light’s frequency and power, you can calculate the energy of each photon and the number of photons emitted per second.

CBSE: Class 12

Example 2

  • The work function of caesium is 2.14 eV; part (a) uses ϕ = hν0​ to get the threshold frequency ν0 = 5.16 × 1014 Hz.
  • This means: below this frequency, no photoelectrons are emitted regardless of intensity.
  • Part (b) uses Einstein’s equation eV0 = hν − ϕ = hc/λ − ϕ with a stopping potential of 0.60 V to find the wavelength of the incident light, which comes out as 454 nm.

So this example shows how work function, threshold frequency, stopping potential, and wavelength are linked in photoelectric effect numericals.

Related QuestionsVIEW ALL [15]

A 100 W sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on it. The wavelength of the sodium light is 589 nm.

(a) What is the energy per photon associated with the sodium light?

(b) At what rate are the photons delivered to the sphere?

There are two sources of light, each emitting with a power of 100 W. One emits X-rays of wavelength 1 nm and the other visible light at 500 nm. Find the ratio of number of photons of X-rays to the photons of visible light of the given wavelength?

A source of monochromatic light liberates 9 × 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:

Monochromatic light of wavelength 632.8 nm is produced by a helium-neon laser. The power emitted is 9.42 mW.

  1. Find the energy and momentum of each photon in the light beam.
  2. How many photons per second, on average, arrive at a target irradiated by this beam? (Assume the beam to have uniform cross-section which is less than the target area.)
  3. How fast does a hydrogen atom have to travel in order to have the same momentum as that of the photon?

The energy of a photon of wavelength 663 nm is ______.

The number of photons per second on an average emitted by the source of monochromatic light of wavelength 600 nm, when it delivers the power of 3.3 × 10−3 watts will be ______ (h = 6.6 × 10−34 Js).

(a) An X-ray tube produces a continuous spectrum of radiation with its short wavelength end at 0.45 Å. What is the maximum energy of a photon in the radiation?

(b) From your answer to (a), guess what order of accelerating voltage (for electrons) is required in such a tube?

The energy flux of sunlight reaching the surface of the earth is 1.388 × 103 W/m2. How many photons (nearly) per square metre are incident on the Earth per second? Assume that the photons in the sunlight have an average wavelength of 550 nm.

Advertisements
Share
Notifications

Englishहिंदीमराठी
Login
Create free account


      Forgot password?
Course
Use app×