Electrons in a certain energy level n=n₁ , can emit 3 spectral lines. When they are in another energy level, n=n₂ they can emit 6 spectral lines. The orbital speed of the electrons in the orbits are in the ratio

Step-by-step solution

Number of emitted spectral lines aligned N &= n(n-1) 2 & 1st case & &=3 & & & & &= n₁ (n₁-1 ) 2 (n₁-3 ) (n₁+2 ) &=0 n₁=3, n₁ &=-2 aligned Negative value of n₁ is not possible aligned & & n₁ &=3 2nd case & N &=6 & Again, & 6 &= n₂ (n₂-1 ) 2 & n₂²-n₂-12 &=0 (n₂-4 ) (n₂+3 ) &=0 n₂=4, n₂ &=-3 aligned Again, as n₂ is always positive n₂=4 Velocity of electron v= Z e² 2 ₀ h n v₁ v₂ = n₂ n₁ v₁ v₂ = 4 3