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If the kinetic energy of an electron inc...

If the kinetic energy of an electron increases by nine times, the wavelength of the de Broglie wave associated with it will increase by how many times?

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The de Broglie wavelength associated with a moving electron of mass m annd kinetic energy E is given by.
`lamda=(h)/(sqrt(2Em))`
Now `lamda_(1)=(h)/(sqrt(2Em)),lamda_(2)=(h)/(sqrt(2xx9Exxm))=(h)/(sqrt(2eM))xx(1)/(3)`
`therefore (lamda_(2))/(lamda_(1))=(h)/(sqrt(2Em))xx(1)/(3)+(h)/(sqrt(2Em)) or, lamda_(2)=(1)/(3)lamda_(1)`
so, de Broglie wave associated with the electron will increase by `1/3` times.
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Knowledge Check

  • 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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    B
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    A
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    D
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  • Statement I: If the kinetic energy of particles with different masses are same, then the de Broglie wavelength of the particles are inversely proportional to their mass Statement II: Momentum of moving particles is inversely proportional to their de Broglie wavelengths.

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