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

A) $10^{34}$
B) $10^{27}$
C) $10^{17}$
D) $10^{- 10}$
Explanation

(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, $\lambda_{e} = \frac{h}{\sqrt{2m_{e}K}}$ …(i)
For the person Mass, $m = 66kg$
Speed, $v = 100kmhr^{- 1} = 100 \times \frac{5}{18}ms^{- 1}$
de Broglie wavelength, $\lambda = \frac{h}{mv}$ …(ii)
Diving (i) by (ii), we get
$\frac{\lambda_{e}}{\lambda} = \frac{h}{\sqrt{2m_{e}K}} \times \frac{mv}{h} = \frac{mv}{\sqrt{2m_{e}K}}$
$= \frac{66 \times 100 \times \frac{5}{18}}{\sqrt{2 \times 9.11 \times 10^{- 31} \times 10 \times 1.6 \times 10^{- 19}}} = 1.07 \times 10^{27}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.