Physics · Modern Physics

Dual Nature of Matter and Radiation formulas for JEE

Every Dual Nature of Matter and Radiation formula you need for JEE, grouped by concept.

FormulasRevision notes
17 formulas2 concepts
01Photoelectric Effect02Matter Waves and de Broglie Relation
01

Photoelectric Effect

13 formulas

Power of Light Beam

P=NE=NhνP = N E = N h\nu

Total transmitted power of a light beam given the number of photons emitted per second.

applies whenMonochromatic light beam.
powerphoton-flux

De Broglie Wavelength

λ=hp=hmv\lambda = \frac{h}{p} = \frac{h}{mv}

Wavelength of a matter wave associated with a moving material particle.

applies whenNon-relativistic speeds (v≪cv \ll c) if p=mvp=mv is used directly.
de-brogliematter-waves

Intensity and Photon Flux

I=nhν=nhcλI = n h \nu = \frac{n h c}{\lambda}

Intensity of a light beam expressed via photon flux nn (number of photons per unit area per unit time).

applies whenUniform monochromatic beam.
intensityphoton-fluxjee-advanced

Combined Photoelectric Equation

12mvmax2=eV0=h(ν−ν0)\frac{1}{2}mv_{max}^2 = eV_0 = h(\nu - \nu_0)

Comprehensive expansion of Einstein's photoelectric equation linking velocity, stopping potential, and threshold frequency.

photoelectriccomprehensivevelocity

Einstein's Photoelectric Equation

Kmax=hν−ϕ0K_{max} = h\nu - \phi_0

Relates the maximum kinetic energy of emitted photoelectrons to incident photon energy and the material's work function.

applies whenIncident frequency must be strictly greater than threshold frequency (ν>ν0\nu > \nu_0).
photoelectriceinsteinwork-function

Incident Wavelength from Stopping Potential

λ=hceV0+ϕ0\lambda = \frac{hc}{eV_0 + \phi_0}

Rearranged photoelectric equation to directly find incident wavelength based on stopping potential and work function.

wavelengthstopping-potential

Photon Energy

E=hν=hcλE = h\nu = \frac{hc}{\lambda}

Energy of a single photon in terms of its frequency and wavelength.

photonenergywavelength

Photon Momentum

p=hνc=hλp = \frac{h\nu}{c} = \frac{h}{\lambda}

Momentum of a single photon.

applies whenValid strictly for massless particles travelling at the speed of light.
photonmomentum

Radiation Pressure (Perfectly Absorbing)

Pr=IcP_r = \frac{I}{c}

Pressure exerted by an electromagnetic wave on a perfectly absorbing black surface.

applies whenNormal incidence on a perfectly absorbing surface.
radiation-pressureabsorbingintensityjee-advanced

Radiation Pressure (Perfectly Reflecting)

Pr=2IcP_r = \frac{2I}{c}

Pressure exerted by an electromagnetic wave on a perfectly reflecting mirror surface.

applies whenNormal incidence on a perfectly reflecting surface.
radiation-pressurereflectingintensityjee-advanced

Stopping Potential Relation

Kmax=eV0K_{max} = e V_0

Relates the maximum kinetic energy of emitted photoelectrons to the required stopping potential.

applies whenValid for the most energetic photoelectrons reaching the collector.
stopping-potentialkinetic-energy

Stopping Potential vs Frequency

V0=(he)ν−ϕ0eV_0 = \left(\frac{h}{e}\right)\nu - \frac{\phi_0}{e}

Linear equation representing stopping potential as a function of incident frequency.

applies whenν≥ν0\nu \geq \nu_0
stopping-potentialgraphslope

Threshold Frequency

ν0=ϕ0h\nu_0 = \frac{\phi_0}{h}

Minimum frequency of incident radiation required to overcome the work function for photoelectric emission.

applies whenDepends uniquely on the nature of the photosensitive material.
thresholdfrequencywork-function
02

Matter Waves and de Broglie Relation

4 formulas

De Broglie Wavelength

λ=hp=hmv\lambda = \frac{h}{p} = \frac{h}{mv}

Wavelength of a matter wave associated with a moving material particle.

applies whenNon-relativistic speeds (v≪cv \ll c) if p=mvp=mv is used directly.
de-brogliematter-waves

De Broglie Wavelength (Accelerated Charge)

λ=h2mqV\lambda = \frac{h}{\sqrt{2mqV}}

De Broglie wavelength of a charge accelerated from rest through a potential difference V.

applies whenParticle starts from rest; non-relativistic limits.
de-broglieaccelerated-chargejee-advanced

De Broglie Wavelength (Thermal Particle)

λ=h3mkT\lambda = \frac{h}{\sqrt{3mkT}}

De Broglie wavelength of a gas molecule or thermal neutron in equilibrium at absolute temperature T.

applies whenIdeal gas behaviour in thermal equilibrium.
de-brogliethermaltemperaturejee-advanced

De Broglie Wavelength (Kinetic Energy)

λ=h2mK\lambda = \frac{h}{\sqrt{2mK}}

De Broglie wavelength of a particle expressed in terms of its kinetic energy.

applies whenNon-relativistic limits.
de-brogliekinetic-energyjee-advanced
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