Compute the shortest wavelength radiation in the Balmer series? What value of n must be used?  (Ans: 364.5 nm & n = ∞)

 


Data Given:

Balmer Series:

∴ Rydberg constant = R = 1.0974 ｘ 10⁷ m⁻¹


To Find:

(a) Shortest Wavelength in Balmer Series = λmin =  ?

(b) Energy level = n = ?



Solution:

Rydberg formula for Balmer Series:

1λ = R( 12²-1n²) -----(1)

where n = 3,4,5,..............


To find the Shortest Wavelength λmin, the energy level n = ∞ is used. (It means the electron jumps from infinite orbital to orbital no. 1)

by putting values

1λmin = 1.0974 ｘ 10⁷ m⁻¹ ( 12²-1∞²)


1λmin = 1.0974 ｘ 10⁷ m⁻¹ ( 14-0)


1λmin = 1.0974ｘ10⁷m⁻¹4    


by flipping the fraction on both sides of the equation we get


λmin =  41.0974ｘ10⁷m⁻¹


or


λmin = 3.6449 ｘ 10⁻⁷ m


or


λmin = 364.5 ｘ 10⁻⁹ m


λmin = 364.5 nm 
and the excited energy level n = ∞------------Ans.



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