The de Broglie wavelength of the electron in the ground state is ₁ and that in the n = 3 level is ₃ then ₃ is given by

Step-by-step solution

According to Bohr's quantization condition: mvr = nh 2 The de Broglie wavelength of an electron is given by = h mv . Substituting mv = h into the quantization condition, we get: 2 r = n = 2 r n In a hydrogen-like atom, the radius of the n -th orbit is proportional to n^2 , so r_n = r₁ n^2 . Therefore, the de Broglie wavelength in the n -th orbit is: _n = 2 (r₁ n^2) n = n(2 r₁) For the ground state ( n=1 ), ₁ = 2 r₁ . For the n=3 level, the de Broglie wavelength is: ₃ = 3(2 r₁) = 3 ₁ Answer: 3 ₁