Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

If λ is the longest wavelength of Lyman series, the shortest wavelength line that of the Balmer series is:
A. 5λ
B. 2λ
C. 4λ
D. 3λ

Answer
VerifiedVerified
483k+ views
like imagedislike image
Hint: In this question you are asked to find the shortest wavelength line of the Balmer series, which can be find by putting the values of the values of n1 and n2 for the shortest wavelength in the Balmer series. It is important that you should know the general formula for wavelength to find the shortest wavelength of the Balmer series as well as longest wavelength of the Lyman series.

Formula used:
For longest wavelength in Lyman series (i.e., first line), the energy difference in two states showing transition should be minimum, i.e, n2 = 2
1λ=R[1n121n22]
Where, R is the Rydberg constant.
λ is the wavelength.

Complete step by step answer:
General formula for wavelength of Lyman series is given as,
1λ=R[1n121n22]
Now, formula for longest wavelength of Lyman series is given as,
n1 = 1 and n1 = 2
1λL=R[112122]1λL=R[1114]1λL=3R4
Now according to the question, If λis the longest wavelength of Lyman series
therefore,
λL=43R=λ4R=3λ...(i)
Now, formula for the shortest wavelength line that of the Balmer series is given as,
n1 =2 and n2=
1λB=R[12212]1λB=R4λB=4R...(ii)
Now, from equations (i) and (ii), we get,
λB=3λ

Hence, option D is the correct option.

Note:It is important to note that the Lyman series is the first series while the Balmer series is the second series, in a hydrogen atom. Most of the students tend to make mistakes in the lowest states of these two states. The lowest state in the Lyman series is 1 while in the Balmer series it is 2. Again, it should be remembered that the spectral lines of Lyman series are ultra-violet while the spectral lines of Balmer series are visible.
Latest Vedantu courses for you
Grade 7 | CBSE | SCHOOL | English
Vedantu 7 CBSE Pro Course - (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for CBSE students
MathsMaths
EnglishEnglish
ScienceScience
₹49,800 (15% Off)
₹42,330 per year
Select and buy