Hydrogen Spectrum JEE Concept — Which Series Has Bigger λ? ⚡

❓ Concept

🎬 Largest Wavelength: Lyman vs Balmer — Hydrogen Spectrum in 59 Sec

Hydrogen atom mein itni saari spectral lines hoti hain…
par exam mein sawal hota hai 👇
👉 Sabse badi wavelength kis series se aati hai? 🌈🤔

Is concept ko samajh liya,
toh ratio-based spectrum questions instant ho jaate hain ⚡

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🖼️ Concept Image

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✍️ Short Explanation

Yeh question ratta nahi,
energy-gap logic ka test hota hai.
Bas yeh yaad rakho:
👉 Badi wavelength = chhota energy gap.

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🔹 Step 1 — Hydrogen Spectral Series Basics

Har spectral series ka final energy level fixed hota hai:

• Lyman series → final level $n = 1$
  

• Balmer series → final level $n = 2$
  

📌 Transitions higher level → final level ke beech hote hain.

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🔹 Step 2 — Energy–Wavelength Relation (FOUNDATION 💯)**

Photon energy:

$$E=\frac{hc}{\mathrm{\lambda }}$$

Iska matlab:

$$\lambda \propto \frac{1}{\mathrm{\Delta }\mathrm{E}}$$

📌 Largest wavelength ⇔ smallest energy difference

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🔹 Step 3 — Smallest Energy Gap in Any Series

Har spectral series mein:

• Sabse chhota energy gap hota hai

• Jab electron just next level se aata hai

👉 Matlab:

$$(n=\text{final}+1)\to (\text{final})$$

So:

• Lyman: $2 \rightarrow 1$
  

• Balmer: $3 \rightarrow 2$
  

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🔹 Step 4 — Compare Lyman & Balmer (CORE IDEA 🔥)**

Hydrogen energy levels:

$$E_n\propto -\frac{1}{n^{\mathrm{2}}}$$

Observe:

• $n=1$ ke paas levels zyada spaced

• $n=2$ ke paas levels closer

👉 Isliye:

• Lyman series ka $\Delta E$ bada

• Balmer series ka $\Delta E$ chhota

📌 Chhota $\Delta E$ ⇒ badi $\lambda$

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🔹 Step 5 — Final Comparison Result

✔️ Largest wavelength of Balmer series
✔️ Largest wavelength of Lyman series se zyada hoti hai

🧠 One-line logic:

Higher final energy level ⇒ smaller energy gap ⇒ larger wavelength

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⭐ Golden Summary Box

• Wavelength $\lambda \propto 1/\Delta E$
  

• Largest $\lambda$ ⇒ smallest $\Delta E$
  

• Smallest $\Delta E$ occurs at
  $(n=\text{final}+1)\rightarrow(\text{final})$
  

• Balmer ($n=2$) gaps < Lyman ($n=1$) gaps

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✅ Final Takeaway

Agar question bole:

Largest wavelength: Lyman vs Balmer?

👉 Turant yaad karo:

$$\boxed{{\displaystyle {\lambda }_{\text{Balmer(max)}}>{\lambda }_{\text{Lyman(max)}}}}$$

No calculation.
No confusion.
Pure concept = pure marks 🚀