A) \[2.7\times {{10}^{-18}}m{{s}^{-1}}\]
B) \[9\times {{10}^{-2}}m{{s}^{-1}}\]
C) \[3\times {{10}^{-31}}m{{s}^{-1}}\
D) \[2.7\times {{10}^{-21}}m{{s}^{-1}}\]
Correct Answer: B
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 |
| \[{{m}_{e}}=9.1\times {{10}^{-31}}kg,{{v}_{e}}=3\times {{10}^{6}}m/s,\] |
| \[m=1mg=1\times {{10}^{-6}}kg\] |
| \[v=\frac{9.1\times {{10}^{-31}}\times 3\times {{10}^{6}}}{1\times {{10}^{-6}}}\] |
| \[=2.7\times {{10}^{-18}}m{{s}^{-1}}\]\[v=\frac{9.1\times {{10}^{-31}}\times 3\times {{10}^{6}}}{1\times {{10}^{-6}}}\] |
| (Mass of electron \[=9.1\times {{10}^{-}}^{31}kg\]) |
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