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What is the ratio of wavelength of second line of Lyman series to that of series limit of Paschen series of H-atom?

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Important Questions on Structure of Atom

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The De-Broglie equation suggests that an electron has
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The wavelength of a charged particle ________ the square root of the potential difference through which it is accelerated.
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What will be the wavelength of the de-Broglie wave associated with, if the kinetic energy of an electron is increased 4 times?
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What will be the associated wavelength, if a 0.66kg ball is moving with a speed of 100m/sh=6.6×10-34Js

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The de-Broglie wavelength associated with a ball of mass 1 kg having kinetic energy 0.5 J is
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The speed of a proton is one hundredth of the speed of light in vaccum. What is the De-Broglie wavelength of the proton? Assume that one mole of protons has a mass equal to one gram. [h=6.626×10-27erg sec]
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What possibly can be the ratio of the de Broglie wavelengths for two electrons each having zero initial energy and accelerated through 50 volts and 200 volts ?

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A helium molecule is moving with a velocity of 2.40×102 ms-1 at 300 K. The De-Broglie wavelength is about