Electrons in a certain energy level n ⁡ = n ⁡ 1 , can emit 3 spectral lines. When they are in another energy level, n ⁡ = n ⁡ 2 , they can emit 6 spectral lines. The ratio of orbital speeds of the electrons is

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Correct answer: A. 4 : 3

Number of emitted spectral lines, N = n ( n - 1 ) 2 . Case I N = 3 ⇒ 3 = n 1 ( n 1 - 1 ) 2 ⇒ n 1 2 - n 1 - 6 = 0 ⇒ ( n 1 - 3 ) ( n 1 + 2 ) = 0 ⇒ n 1 = 3 Case II N = 6 ⇒ 6 = n 2 ( n 2 - 1 ) 2 ⇒ n 2 2 - n 2 - 12 = 0 ⇒ ( n 2 - 4 ) ( n 2 + 3 ) = 0 ⇒ n 2 = 4 Velocity of electron v = Z e 2 2 ε 0 h n ∴ v 1 v 2 = n 2 n 1 ⇒ v 1 v 2 = 4 3

Electrons in a certain energy level n ⁡ = n ⁡ 1 , can emit 3 spectral lines. When they are in another energy level, n ⁡ = n ⁡ 2 , they can emit 6 spectral lines. The ratio of orbital speeds of the electrons is

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