In accordance with the Bohr's model, the quantum number that characterises the Earth's revolution around the Sun in an orbit of radius 1.5 10¹¹ ~m with orbital speed 3 10^4 ~ms ⁻¹ is [given, mass of Earth =6 10²⁴ ~kg ]

Step-by-step solution

Given, v=3 10^4 ~m / s aligned r & =1.5 10¹¹ ~m m_e & =6 10²⁴ ~kg aligned According Bohr's atomic model, Angular momentum =m v r= n h 2 where, h= Planck's constant =6.62 10⁻³⁴ ~J - s and n= quantum number aligned n & = 2 (m_e v r ) h & = 2 314 6 10²⁴ 3 10^4 1.5 10¹¹ 6.62 10⁻³⁴ & =2.57 10⁷⁴ aligned Hence, the quantam number that characterises the Earth's revolution is 2.57 10⁷⁴ .