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Dual Nature Of Radiation And Matter

Question
CBSEENPH12039712
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An electromagnetic wave of frequency ν = 3.0 MHz passes from vacuum into a dielectric medium with permittivity ε = 4.0. Then

  • wavelength is doubled and the frequency remains unchanged

  • wavelength is doubled and frequency becomes half

  • wavelength is halved and frequency remains unchanged

  • wavelength and frequency both remain unchanged.

Solution

C.

wavelength is halved and frequency remains unchanged

In vacuum, ε0 = 1
In medium, ε = 4
So, refractive index
straight mu space equals space square root of straight epsilon divided by straight epsilon subscript 0 end root space equals space square root of 4 divided by 1 end root space equals space 2 wavelength space straight lambda to the power of apostrophe space equals space straight lambda over straight mu space equals space straight lambda over 2 and space wave space velocity space straight v equals space straight c over straight mu space equals straight c over 2
Hence, it is clear that wavelength and velocity will become half but frequency remains unchanged when the wave is passing through any medium.

Some More Questions From Dual Nature of Radiation and Matter Chapter

Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see in the figure).



If a strong diffraction peak is observed when electrons are incident at an angle ‘i’ from the normal to the crystal planes with distance’ between them (see figure), de Broglie wavelength λdB of electrons can be calculated by the relationship (n is an integer) 

Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see in the figure).



In an experiment, electrons are made to pass through a narrow slit of width’ comparable to their de Broglie wavelength. They are detected on a screen at a distance ‘D’ from the slit (see figure). 

Which of the following graph can be expected to represent the number of electrons ‘N’ detected as a function of the detector position ‘y’(y = 0 corresponds to the middle of the slit)? 

The time by a photoelectron to come out after the photon strikes is approximately

An alpha nucleus of energy 1 /2 mv2 bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to 

If I0 is the intensity of the principal maximum in the single slit diffraction pattern, then what will be its intensity when the slit width is doubled?

The maximum number of possible interference maxima for slit-separation equal to twice the wavelength in Young’s double-slit experiment is

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