Question

The ratio of the de Broglie wavelengths of an electron of energy $10eV$ to that of person of mass $66kg$ travelling at a speed of $100km/h$ is of the order of

• A. $10^{34}$
• B. $10^{27}$
• C. $10^{17}$
• D. $10^{-10}$

Answer 1

Answer: (B)

For an electron Mass,
$m_e=9.11\times 10^{-31}kg$,
Kinetic energy, $K=10eV$
$=10\times 1.6\times 10^{-19}J$
de Broglie wavelength,
${\lambda }_e=\frac{h}{\sqrt{2m_{e}K}}\dots$(i)
For the person
Mass, $m=66kg$,
Speed, $v=100km{h}^{-1}=100\times \frac{5}{18}m{s}^{-1}$
de Broglie wavelength, $\lambda =\frac{h}{mv}\dots$(ii)
Divide (i) by (ii), we get
$\frac{{\lambda }_e}{\lambda }=\frac{h}{\sqrt{2m_{e}K}}\times \frac{mv}{h}$
$=\frac{mv}{\sqrt{2m_{e}K}}$
$=\frac{66\times 100\times \frac{5}{18}}{\sqrt{2\times 9.11\times 10^{-31}\times 10\times 1.6\times 10^{-19}}}$
$=1.07\times 10^{27}$