An electron in the ground state of the hydrogen atom has the orbital radius of 5.3 × 1 0 − 11 m while that for the electron in third excited state is 8.48 × 1 0 − 10 m . The ratio of the de Broglie wa

Question

An electron in the ground state of the hydrogen atom has the orbital radius of 5.3 × 1 0 − 11 m while that for the electron in third excited state is 8.48 × 1 0 − 10 m . The ratio of the de Broglie wavelengths of electron in the excited state to that in the ground state is

TestHub · Accepted Answer

λ = mv h ​ ​ mvr = 2 π nh ​ mv = 2 π r nh ​ λ = nh 2 π rh ​ λ ∝ n r ​ λ 4 ​ λ 1 ​ ​ = n 1 ​ r 4 ​ r 1 ​ n 4 ​ ​ = 1 × 84.8 × 1 0 − 11 5.3 × 1 0 − 11 × 4 ​ λ 4 ​ λ 1 ​ ​ = 4 1 ​ ​

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