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

What is the shortest wavelength present in the Paschen series of spectral lines.

Answer
VerifiedVerified
485.7k+ views
2 likes
like imagedislike image
Hint: The Paschen series are the series of lines in the spectrum which are emitted when the atoms of the hydrogen correspond to transitions between the different states with principal quantum number n=3 and higher states.

Formula used:The formula of the Rydberg’s formula is given by,
hcλ=2176×1019×(1n121n22)

Where the Planck’s constant is h, the speed of light is c, the wavelength is λ and the number of the spectral lines is n1andn2.

Complete answer:
It is asked in the problem what is the shortest wavelength present in the Paschen series of spectral lines.
The Paschen series is the spectral line which corresponds to the electrons which transits from the higher energy line to the lower energy line i.e. n=3.

The formula of the Rydberg’s formula is given by,

hcλ=2176×1019×(1n121n22)

Where the Planck’s constant is h, the speed of light is c, the wavelength is λ and the number of the spectral lines is n1andn2.

Here the spectral series will start from n1=3 and as we need to calculate the value of least wavelength of spectrum therefore, n2= replacing these values in the Rydberg’s formula we get.

hcλ=2176×1019×(1n121n22)
hcλ=2176×1019×(13212)
hcλ=2176×1019×(1320)
hcλ=2176×1019×19
hcλ=2418×1019
λ=hc2418×1019

Replacing the values of the Planck’s constant and speed of light we get,

λ=hc2418×1019
λ=6626×1034×3×1082418×1019
λ=6626×1034×3×108×10+192418
λ=820×107m
λ=820×109m
λ=820nm.

The shortest wavelength of the Paschen series is equal to λ=820nm.

Note: When the electrons transits in different states then a spectrum of lines are recorded and these are known as Paschen series if the principal quantum number is more than n=3. The spectral series is the wavelength of the electromagnetic radiation arranged in the sequence.
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 (9% Off)
₹45,300 per year
Select and buy