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  4. If the kinetic energy of the particle is increased by 16 times, the percentage change in the de-Broglie wavelength of the particle is

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Q. If the kinetic energy of the particle is increased by 16 times, the percentage change in the de-Broglie wavelength of the particle is

CMC MedicalCMC Medical 2008

Solution:

From de-Broglies formula $ \lambda =\frac{h}{p}=\frac{h}{\sqrt{2mK}} $ $ \frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{\sqrt{{{K}_{2}}}}{\sqrt{{{K}_{1}}}} $ Given, $ {{K}_{2}}=16{{K}_{1}} $ $ \therefore $ $ \frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\sqrt{16}=4 $ $ \Rightarrow $ $ {{\lambda }_{2}}=\frac{{{\lambda }_{1}}}{4} $ % change $ =\frac{{{\lambda }_{2}}-{{\lambda }_{1}}}{{{\lambda }_{1}}}\times 100 $ % change $ =\frac{3}{4}\times 100=75% $