• # question_answer Find the de-Broglie wavelength of Earth. Mass of Earth is$6\times {{10}^{24}}\,kg$. Mean orbital radius of Earth around Sun is$150\,\,\times \,\,{{10}^{6}}\,km$. A) $3.7\,m$                      B) $3.7\,\,\times \,\,{{10}^{-63}}m$C) $3.7\times {{10}^{63}}\,m$                D) $3.7\times {{10}^{-63}}cm$

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.