12.10 In accordance with the Bohr’s model, find the quantum number that characterizes the earth’s revolution around the sun in an orbit of radius 1.5 × 1011 m with orbital speed 3 × 104 m/s. (Mass of earth = 6.0 × 1024 kg.)

Hint: In Bohr's model of atom, the angular momentum is quantized.
Step 1: Find the relation between the angular momentum and the quantum number.
The radius of the orbit of the Earth around the Sun, r=1.5x1011m
The orbital speed of the Earth, v = 3 x 104 m/s
Mass of the Earth, m=6.0 x 1024 kg
According to Bohr's model, angular momentum is quantized and given as:
mvr=nh2π
where,
h = Planck's constant = 6.62×10-34  J-s
n = Quantum number
Step 2: Find the quantum number corresponding to the earth revolution around the sun.
n=(mvr)2πh=2π×6×1024×3×104×1.5×10116.62×10-34=25.61×1073=2.6×1074
Hence, the quantum number that characterizes the Earth's revolution is 2.6×1074.