Question

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