I found an answer from www.quora.com

Which **series** of hydrogen spectrum will have **shortest wavelength** ...

Transition between lyman and balmer will have **shortest wavelength** Dont learn ...
Apurva N. Saraogi, Technical Executive at CSEA, IIT Guwahati (2017-**present**) ...
that wavelength of lyman is always shorter than balmer than **paschen** followed by
... In the **spectral series** of hydrogen, as the wavelength decreases the **lines** ...

For more information, see Which **series** of hydrogen spectrum will have **shortest wavelength** ...

I found an answer from en.wikipedia.org

Hydrogen **spectral series** - Wikipedia

The Paschen **lines** all lie in the infrared band. ... overlaps with the next (Brackett)
series, i.e. the **shortest line** in the Brackett series has a **wavelength** that falls
among the **Paschen series**.

For more information, see Hydrogen **spectral series** - Wikipedia

I found an answer from www.britannica.com

**Spectral line series** | physics | Britannica

Feb 25, 2021 **...** **Spectral line series**, any of the related sequences of wavelengths ... in spacing,
coming closer together toward the **shortest wavelength**, called the **series** limit. ...
The Lyman **series** lies in the ultraviolet, whereas the **Paschen**, ...

For more information, see **Spectral line series** | physics | Britannica

I found an answer from byjus.com

Spectral **Series**- Explained along with **Hydrogen spectrum**, **Rydberg** ...

Visit BYJU'S to know about **Rydberg formula**, **Hydrogen** spectral series like,
Lyman, ... **Physics** Important Questions ... 𝜆 is the **wavelength**; R is the **Rydberg**
**constant** has the value 1.09737✕10^{7} m^{-1}; Z is the **atomic** number ... All the
**wavelength of Paschen series** falls in the Infrared region of the electromagnetic
**spectrum**.

For more information, see Spectral **Series**- Explained along with **Hydrogen spectrum**, **Rydberg** ...

Rydberg formula [math]

As per the third postulate of Bohr's model, if an atom moves from a higher energy state with quantum number \left(n_2\right) to a lower energy state with quantum number\left(n_1\right), the difference in energy is taken away by a photon of frequency \upsilon_{hl} . The frequency of any line in a series is a two-term difference.

[math]h\upsilon_{hl}=\frac{me^4}{8\epsilon_0^2h^2}[\frac{1}{n_1^2}-\frac{1}{n_2^2}][/math] where, Rydberg constant R = \frac{m e^4}{8 \epsilon_0^2 h^2} = 13.6 eV = 21.76 *10^{-19} J

A line spectrum of different series is emitted by the atomic hydrogen.

Paschen series: [math]\upsilon=R\left[\frac{1}{3^2}-\frac{1}{n_2^2}\right][/math]; n_2 = 4, 5, 6............

Read more:https://byjus.com/physics/spectral-series/

Step 1: Set up an equation for shortest wavelengths of Paschen series

[math]h\upsilon_{hl}=R[\frac{1}{n_1^2}-\frac{1}{n_2^2}][/math]

[math]\frac{hc}{\lambda_{hl}}=R[\frac{1}{n_1^2}-\frac{1}{n_2^2}][/math] \because \upsilon = \frac{c}{\lambda}

[math]\lambda_{hl}=\frac{hc}{R[\frac{1}{n_1^2}-\frac{1}{n_2^2}]}[/math]

Step 2: plug in the known values in the above equation

Lower quantum number n_1 = 3 , Higher quantum number \ n_2=\infty, Planck constant h = 6.64 * 10^{-34} , speed of light c = 3* 10^{8}

[math]\lambda_{hl}=\frac{6.64*10^{-34}*3*10^8}{21.76*10^{-19}[\frac{1}{3^2}-\frac{1}{\infty^2}]}[/math]

\lambda _{hl} = \frac{1.992 * 10^{-25}}{2.42*10^{-19}}

\lambda _{hl} = 8.23 * 10^{-7} m

Hence, shortest wavelength in Paschen series \lambda _{hl} = 8.23 * 10^{-7} m