This chapter explores the dual nature of radiation and matter, focusing on how light behaves both as a wave and a particle. Understanding this duality is key to grasping modern physics concepts.
DUAL NATURE OF RADIATION AND MATTER – Formula & Equation Sheet
Essential formulas and equations from Physics Part - II, tailored for Class 12 in Physics.
This one-pager compiles key formulas and equations from the DUAL NATURE OF RADIATION AND MATTER chapter of Physics Part - II. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Key concepts & formulas
Essential formulas, key terms, and important concepts for quick reference and revision.
Formulas
E = hν
E is the energy of a photon (in joules), h is Planck's constant (6.626 × 10⁻³⁴ J·s), and ν is the frequency of light (in hertz). This equation relates the energy of a photon to its frequency, illustrating the quantum nature of light.
K_max = hν - φ
K_max is the maximum kinetic energy of the emitted photoelectrons (in joules), ν is the frequency of the incident light (in hertz), and φ is the work function of the material (in joules). This equation explains how much kinetic energy the electrons gain during photoelectric emission.
φ = eV_0
φ is the work function (in joules), e is the charge of an electron (1.602 × 10⁻¹⁹ C), and V_0 is the stopping potential (in volts). This relationship connects the work function to the stopping potential when the photoelectric current stops.
ν_0 = φ/h
ν_0 is the threshold frequency (in hertz), φ is the work function (in joules), and h is Planck's constant. This equation shows the minimum frequency required for photoelectric emission to occur.
p = h/λ
p is the momentum of a photon (in kg·m/s), h is Planck's constant, and λ is the wavelength (in meters). This equation describes the momentum associated with electromagnetic radiation.
λ = c/ν
λ is the wavelength (in meters), c is the speed of light (≈ 3 × 10⁸ m/s), and ν is the frequency of the light (in hertz). This basic wave relation allows calculation of wavelength from frequency.
K_max = (1/2)mv²
K_max is the maximum kinetic energy of the emitted photoelectrons (in joules), m is the mass of the electron (9.11 × 10⁻³¹ kg), and v is the velocity of the photoelectrons (in m/s). This equation can be used to relate the kinetic energy of ejected electrons to their velocity.
V_0 = K_max/e
V_0 is the stopping potential (in volts), K_max is the maximum kinetic energy (in joules), and e is the charge of an electron. This equation provides a way to determine the stopping potential from the maximum kinetic energy of emitted electrons.
λ = h/p
λ is the de Broglie wavelength (in meters), h is Planck's constant, and p is the momentum of the particle (in kg·m/s). This relationship illustrates the wave nature of matter, specifically for particles such as electrons.
n_0 = 0φ/h
n_0 is the threshold frequency (in hertz), φ is the work function (in joules), and h is Planck's constant. This relates the threshold frequency to the work function, indicating the minimum frequency of light required to eject an electron from a material.
Equations
K_max = eV_0
This states that the maximum kinetic energy of the emitted photoelectrons is equal to the charge of the electron multiplied by the stopping potential, clearly establishing a relation between the photoelectric effect and electric potential.
eV_0 = hf - φ
Here, eV_0 equals the energy gained by the photoelectrons when they are stopped by the electric field, relating stopping potential directly to the frequency of incident light and the material's work function.
E = hf
This describes the energy of a photon emitted or absorbed in terms of its frequency, illustrating yet another clear association between energy and electromagnetic radiation.
p = E/c
This expresses momentum p of a photon in terms of its energy E and the speed of light c, allowing movement between energy and momentum calculations of light particles.
ν = c/λ
This fundamental equation expresses the relationship of the speed of light c to the frequency ν of electromagnetic radiation and its wavelength λ, a vital equation in understanding wave motion.
K_max = hf - φ
Directly relates the maximum kinetic energy of emitted electrons to both the frequency of the incoming light and the work function of the material, a core principle in explaining photoelectric emission.
λ = h/(mv)
Relates the de Broglie wavelength of a particle to its mass m and velocity v, a concept unifying classical and quantum physics.
ν_0 = φ/h
Showcases the relationship between threshold frequency and work function in photoelectric emissions, indicating why certain metals react differently to light.
E = m₀c²
Relates rest mass energy to mass m₀ and the speed of light c, important in understanding the energy considerations of mass and electromagnetic radiation.
E = mc²
This famous equation by Einstein indicates the equivalence of mass m (in kg) to energy E (in joules) using the speed of light c, a cornerstone in modern physics demonstrating mass-energy conversion.
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