A) \[2.7\times {{10}^{-18}}\text{m}{{\text{s}}^{-1}}\]
B) \[9\times {{10}^{-2}}\text{m}{{\text{s}}^{-1}}\]
C) \[3\times {{10}^{-31}}\text{m}{{\text{s}}^{-1}}\]
D) \[2.7\times {{10}^{-21}}\text{m}{{\text{s}}^{-1}}\] (Mass of electron\[=\text{ }9.1\times {{10}^{-}}^{31}kg\])
Correct Answer: A
Solution :
Wavelength of a particle is given by\[\lambda =\frac{h}{P}\]where h is Planck's constant and wavelength of an electron is given by \[{{\lambda }_{e}}=\frac{h}{{{p}_{e}}}\]but\[\lambda ={{\lambda }_{e}}\]So,\[p={{p}_{e}}\]or\[mv={{m}_{e}}{{v}_{e}}\] or\[v=\frac{{{m}_{e}}{{v}_{e}}}{m}\]Putting the under given data \[{{m}_{e}}=9.1\times {{10}^{-31}}kg,{{v}_{e}}=3\times {{10}^{6}}m/s,\] \[m=1mg=1\times {{10}^{-6}}kg\] \[v=\frac{9.1\times {{10}^{-31}}\times 3\times {{10}^{6}}}{1\times {{10}^{-6}}}\] \[=2.7\times {{10}^{-18}}m{{s}^{-1}}\]
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