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  4. De Broglie wavelength of a body of mass m and kinetic energy E is given by

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Q. De Broglie wavelength of a body of mass m and kinetic energy E is given by

KCETKCET 1998Dual Nature of Radiation and Matter

Solution:

de Broglie wavelength associated with the particle $\lambda=\frac{ h }{ p }$ where $h$ is the Planck's constant now we know thwt, $E =\frac{1}{2} mv ^{2}$ and $p = mv$ by mutiplying by $m$ on both sides we get,
$p =\sqrt{2 mE }$
hence,
$ \lambda=\frac{ h }{\sqrt{2 mE }} $