Dual Nature Of Radiation And Matter
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A photon of frequency v has a momentum associated with it. If c is the velocity of light, the momentum is
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v /c
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h v c
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h v /c2
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h v /c
D.
h v /c
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According to Einstein’s photoelectric equation, the plot of the kinetic energy of the emitted photo electrons from a metal Vs the frequency, of the incident radiation gives straight line whose slope
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depends on the nature of the metal used
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depends on the intensity of the radiation
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depends both on the intensity of the radiation and the metal used
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is the same for all metals and independent of the intensity of the radiation.
D.
is the same for all metals and independent of the intensity of the radiation.

Einstein's photoelectric equation is
K.E.max = hv − φ ............... (i)
The equation of line is
y = mx + c .............. (ii)
Comparing above two equations m = h, c = - φ
Hence, the slope of the graph is equal to Planck's constant (non-variable) and does not depend on the intensity of radiation.
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
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1/Ze
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v2
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1/m
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1/v4
C.
1/m
An electromagnetic wave of frequency ν = 3.0 MHz passes from vacuum into a dielectric medium with permittivity ε = 4.0. Then
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wavelength is doubled and the frequency remains unchanged
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wavelength is doubled and frequency becomes half
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wavelength is halved and frequency remains unchanged
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wavelength and frequency both remain unchanged.
C.
wavelength is halved and frequency remains unchanged
In vacuum, ε0 = 1
In medium, ε = 4
So, refractive index
Hence, it is clear that wavelength and velocity will become half but frequency remains unchanged when the wave is passing through any medium.
An electron beam is accelerated by a potential difference V to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays.If λmin is the smallest possible wavelength of X-ray in the spectrum, the variation of log λ min with log V is correctly represented in
C.
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