A) \[3.7\,m\]
B) \[3.7\,\,\times \,\,{{10}^{-63}}m\]
C) \[3.7\times {{10}^{63}}\,m\]
D) \[3.7\times {{10}^{-63}}cm\]
Correct Answer: B
Solution :
The Earth revolves around the Sun once a year and its orbit has a mean radius\[150\,\,\times \,\,{{10}^{6}}\,km\]. Hence its average orbital speed is \[v=\frac{2\pi \times 150\times {{10}^{9}}}{365\times 24\times 3600}\,\,=\,\,3\times {{10}^{4}}\,m\,{{s}^{-1}}\] As the Earth has mass \[6\,\,\times \,\,{{10}^{24}}\,kg\], its average momentum is \[p=mv=1.8\times {{10}^{29}}\,kg\,\,m\,{{s}^{-1}}\], and so its de Broglie wavelength is \[\lambda =\frac{h}{p}=\frac{6.63\times {{10}^{-34}}}{1.8\times {{10}^{29}}}=3.7\times {{10}^{-63}}\,m,\] If the Sun can be considered stationary.
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