A) \[\text{1}{{0}^{\text{34}}}\]
B) \[\text{1}{{0}^{\text{27}}}\]
C) \[\text{1}{{0}^{\text{17}}}\]
D) \[\text{1}{{0}^{-\text{1}0}}\]
Correct Answer: B
Solution :
Mass of electron \[{{m}_{e}}=9.11\times {{10}^{-31}}kg\] Kinetic energy \[K=10\,\,eV=10\times 1.6\times {{10}^{-19}}\] \[=1.6\times {{10}^{-18}}J\] de-Broglie wavelength, \[{{\lambda }_{e}}=\frac{h}{\sqrt{2{{m}_{e}}}K}\] ... (i) Mass of man m = 66 kg Speed v = 100 km/h \[=100\times \frac{5}{18}m/s\] de-Broglie wavelength \[\lambda =\frac{h}{mv}\] ... (ii) From Eqs. (i) and (ii), we get \[\frac{{{\lambda }_{e}}}{\lambda }=\frac{h}{\sqrt{2{{m}_{e}}K}}\times \frac{mv}{h}\] \[=\frac{mv}{\sqrt{2{{m}_{e}}K}}\] \[=\frac{66\times 100\times \frac{5}{18}}{\sqrt{2\times 9.11\times {{10}^{-31}}\times 10\times 1.6\times {{10}^{-19}}}}\] \[=\frac{66\times 100\times \frac{5}{18}}{1.7\times {{10}^{-24}}}=1.078\times {{10}^{-27}}\]
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