Dual Nature of Light

Q: Obtains Bohr's quantisation condition for angular momentum of electron orbiting in \$n^{th}\$ hydrogen atom on the basis of the wave picture of an electron using de Broglie hypothesis.

According to De-brogile's wavelength associated with an electron ;\$\lambda =\dfrac{h}{mv}\$......1and the standing wave condition that circumference \$=\$ whole Number of wave length If 'n' is the nth orbit\$\therefore 2\pi r=n\lambda n\$....2\$\therefore \$ since angular momentum \$L=mvr\$ from eqn (1)\$L=\dfrac{hr}{\lambda}\$\$=\dfrac{hr}{\left(\dfrac{2\pi r}{n}\right)}\$ from 1 and 2\$\therefore L=\dfrac{nh}{2\pi}\$ Bohr's Quantization condition

Q: Which of the following phenomenon works on the particle nature of light?

(a) Interference is a phenomenon in which two waves of same frequency superpose to give resultant intensity different from sum of their separate intensity. So, it cannot exhibit particle's nature of light.(b) Diffraction is a phenomenon in which light bends at sharp ends of an obstacle or a hole. So, it also cannot exhibit particle's nature of light.(c) Polarisation of light is a property owing to which a light ray after emerging through a crystal (a special kind like tourmaline) have vibrations in a plane perpendicular to its direction of propagation. So, it also can not explain particle's nature of light.(d) Photoelectric effect states that light travels in the form of bundles or packets of energy, called photons. This effect is explained on the basis of quantum nature of light. So, it clearly explains the particles's nature of lighthence (d) is correct.

Q: What is matter waves? Write any two characteristics of it.

Matter waves: According to De-Broglie, a wave is associated with each moving particle which is called matter waves. This wave has wave length λ=hpλ=hp. Here h is Planck's constant and p is the moment of the moving particle.Characteristics of Matter waves:(i) Lighter the particle, greater is the De-Broglie wave length.(ii) The faster the particle moves, the smaller is its De-Broglie wave length.(iii) The De-Broglie wave length of a particle in independent of the charge or nature of the particle.(iv) The matter waves are not electromagnetic in nature. The electromagnetic waves are produced only by charged particle.

Q: A particle of mass \$1mg\$ has the same wavelength as the electron moving with a velocity of \$3 \times 10^6 ms^{-1}\$. The velocity of the particle is (mass of electron =\$9.1 \times 10^{-31}\$ kg).

\$ \lambda_{particle} = \lambda_{electron}\$\$ \cfrac{h} {m_pV_p} = \cfrac{h}{m_eV_e}\$or, \$ m_pV_p = m_eV_e\$\$ 10^{-6} \times V_p = 9.31 \times 10^{-31} \times 3 \times 10^6\$\$ \therefore V_p = 2.7 \times 10^{-18} ms^{-1}\$

Q: Ray optics is valid when characteristic dimension are

Ray optics is valid when characteristic dimension are much larger than wavelength of light . The size of obstacle must be much larger than the wavelength of light. If wavelength is comparable to the size of object, then diffraction could happen, but it cannot be explained using ray optics, it will require wave theory of light.

Q: A wave or a pulse is reflected normally from the surface of a denser medium back into the rarer medium. The phase change caused by the reflection-

When a wave or a pulse is reflected normally from the surface of a denser medium back into the rarer medium, then tere is a phase difference of \$\pi \$. According to electromagnetic theory When a light beam falls on a boundary of two media, then one part of it will be reflected and other part will be refracted. If refractive index of a medium, where the electromagnetic wave is refracted, is greater than the medium incident, then phase of reflected ray will be reverse with respect to the incident beam. As a result of which the wave suffers a phase change of \$\pi \$.

Q: Which of the following is not a property of light

LIght is electromagnetic in nature it does not require any material medium for its propogation.

Q: Wave theory cannot explain the phenomena ofA) Polarization B) DiffractionC) Compton effect D) Photoelectric effect

Wave theory can explain polarization and diffraction but could not explain compton effect and photoelectric effect. Compton effect and photoelectric effect is explain by quantum theory which treat light as particle.So, the answer is option (C).

Q: Which of the following does not support the wave nature of light?

Photoelectric effect does not support the wave nature of light.Photoelectric effect can be explained only using particle nature of light.

Q: Wave nature of light is demonstrated by :

In the Interference, Diffraction and Polarization phenomenons, the wave nature of light is demonstrated.While in photoelectric effect, we consider light as stream of particles called photons which carries energy with them.