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  4. If kinetic energy of a proton is increased, nine times the wavelength of the de Broglie wave associated with it would become

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Q. If kinetic energy of a proton is increased, nine times the wavelength of the de Broglie wave associated with it would become

Structure of Atom

Solution:

$\lambda=\frac{h}{\sqrt{2 m E}}$
$\frac{\lambda_{1}}{\lambda_{2}}=\sqrt{\frac{E_{2}}{E_{1}}}$
$=\sqrt{\frac{9 E_{1}}{E_{1}}}=3$
$\lambda_{2}=\frac{1}{3} \lambda_{1}$