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

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Solution

Given: The radius of the orbit is 1.5× 10 11 m, the orbital speed of earth is 3× 10 4 m/s, the mass of earth is 6.0× 10 24 kg.

According to Bohr's model, the angular momentum is given as,

mvr= nh 2π n= mvr×2π h

By substituting the given values in the above expression, we get,

n= 2π×6× 10 24 ×3× 10 4 ×1.5× 10 11 6.62× 10 −34 =2.6× 10 74

Thus, the quantum number that characterizes the earth’s revolution is 2.6× 10 74 .

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