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The shortest wavelength of H atom in the Lyman series is λ1. The longest wavelength in the Balmer series of He+ is – (a) 5λ1/9 (b) 36λ1/5 (c) 27λ1/5 (d) 9λ1/5
By BYJU'S Exam Prep
Updated on: September 25th, 2023
The longest wavelength in the Balmer series of He+ is 9λ1/5. Steps to find the longest wavelength in the Balmer series of He+:
We know that:
Shortest wavelength → Max energy (∞ → 1) (Lyman series)
1/λ1 = RH(1)2 [1/1 – 0]
Substituting the values we get:
1/λ1 = RH
On rearranging we get:
RH = 1/λ1
We know that for the Balmer series:
1/λ = RH(2)2 [1/22 – 1/32]
Substituting the values we get:
= RH(4) (9 – 4)/36
= 5RH/9
On simplification:
λ = 9/5RH = 9λ1/5
Therefore the correct answer is an option (d).
Spectral Series
Since the hydrogen atom is the most basic atomic system in nature, it generates the most basic of these series. When a slit is used to allow a beam of light or other radiation to enter the apparatus, each element of the beam or radiation reflects an image of the source. When resolved by a spectroscope, these images can be seen. The images will take the shape of parallel lines that are positioned next to one another with consistent spacing. On the side with higher wavelengths, the lines will be further apart, and as they move from the higher to the lower wavelength side, they will gradually get closer. The series limit is the shortest wavelength with the fewest separated spectral lines.
Lyman Series
The series was started between 1906 and 1914 by Theodore Lyman. It bears his name as a result. The Lyman series, in accordance with Bohr’s theory, emerges when electrons move from higher energy levels (nh = 2,3,4,5,6,…) to nl = 1 energy state. The Lyman series has wavelengths that are all in the ultraviolet region.
Summary:
The shortest wavelength of H atom in the Lyman series is λ1. The longest wavelength in the Balmer series of He+ is – (a) 5λ1/9(b) 36λ1/5(c) 27λ1/5(d) 9λ1/5
The shortest wavelength of the H atom in the Lyman series is λ1. The longest wavelength in the Balmer series of He+ is 9λ1/5. A spectral series is a collection of wavelengths that have been arranged in order.
