In accordance with Bohr's model,find the quan | vedclass

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(D) Given:Radius of the orbit,$r = 1.5 	imes 10^{11} \; m$Orbital speed,$v = 3 	imes 10^{4} \; m/s$Mass of the Earth,$m = 6.0 	imes 10^{24} \; kg$P

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$2.6 	imes 10^{74}$

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(D) Given:Radius of the orbit,$r = 1.5 	imes 10^{11} \; m$Orbital speed,$v = 3 	imes 10^{4} \; m/s$Mass of the Earth,$m = 6.0 	imes 10^{24} \; kg$Planck's constant,$h = 6.626 	imes 10^{-34} \; J \cdot s$According to Bohr's quantization condition for angular momentum:$L = mvr = \frac{nh}{2\pi}$Rearranging for the quantum number $n$:$n = \frac{2\pi mvr}{h}$Substituting the values:$n = \frac{2 	imes 3.1416 	imes (6.0 	imes 10^{24}) 	imes (3 	imes 10^{4}) 	imes (1.5 	imes 10^{11})}{6.626 	imes 10^{-34}}$$n = \frac{169.646 	imes 10^{39}}{6.626 	imes 10^{-34}}$$n \approx 25.603 	imes 10^{73} \approx 2.56 	imes 10^{74}$Rounding to the nearest provided option,we get $n \approx 2.6 	imes 10^{74}$.

In accordance with Bohr's model,find the quantum number that characterizes the Earth's revolution around the Sun in an orbit of radius $1.5 \times 10^{11} \; m$ with an orbital speed of $3 \times 10^{4} \; m/s$. (Mass of Earth $= 6.0 \times 10^{24} \; kg$)

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