d2

17. radius of first Bohr orbit is x (im assuming H-atom)

wavelength of third orbit,

λ=h/mv₃

=> mv₃ = h/λ

now, mv₃r₃ = 3h/2Î

so, r₃/λ = 3/2Î ... (i)

Now r is directly proportional to n²/Z.

=> r₃/x = 3² = 9
=> r₃ = 9x

using this in (i), 9x/λ = 3/2Î

=> λ = 6xÎ

16. answer is 27........

18. shortest wavelength occurs when transition occurs from ∞

So, shortest lyman wavelength 1λ = R

=> x = 1/R ... (i)

Longest wavelength occurs when transition takes place frm just above excited state to the prev, state,

So, longest Balmer wavelength for He⁺
1λ = 4R(12²-13²)

=> 1/λ = 5R/9

=> λ = 9/5R = 9x/5

maths_physco how??