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?

Explanation

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.