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Emission and Absorption Spectra

If E 1, E 2 a...

Question

If $E_{1}, E_{2} a n d E_{3}$ represents the kinetic energy of an electron, an alpha particle and a proton each having same de-Broglie’s wavelength then

A

E_{1} > E_{2} > E_{3}

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B

E_{2} > E_{1} > E_{3}

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C

E_{1} > E_{3} > E_{2}

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D

E_{1} = E_{2} = E_{3}

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Solution

The correct option is C $E_{1} > E_{3} > E_{2}$
de-Broglie’s wave length is given by
$λ = \frac{h}{m V}; V = \frac{h}{m λ}$
$K E = \frac{1}{2} m V^{2} = \frac{1}{2} m {(\frac{h}{m λ})}^{2}$
$K E α \frac{1}{m}$
$H e n c e, E_{1} > E_{3} > E_{2}$

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