An electron in the ground state of the hydrogen atom has the orbital radius of 5.3 × 10⁻¹¹ m while that for the electron in third excited state is 8.48 × 10⁻¹⁰ m. What is the ratio of the de Broglie wavelengths of electron in the ground state to that in excited state?

Using Bohr's theory and de Broglie relation, the de Broglie wavelength λ ∝ n. For ground state (n = 1) and third excited state (n = 4), the ratio λ₁ / λ₄ = 1 / 4. So, the correct answer is 1/4.

JEE Mains 2025 Physics PYQ De Broglie Wavelength – 22nd Jan Shift 1

Keyword Focus: JEE Mains 2025 Physics PYQ De Broglie Wavelength

Are you preparing for JEE Mains 2025? In this article, we break down a real Physics PYQ (Previous Year Question) from the 22nd January Shift 1 paper. This question tests your understanding of the De Broglie wavelength of an electron in the hydrogen atom — a fundamental concept from Atomic Structure in the JEE Physics syllabus.

📘 Question: De Broglie Wavelength of Electron

An electron in the ground state of the hydrogen atom has an orbital radius of 5.3 × 10^–11 m while that for the electron in the third excited state is 8.48 × 10^–10 m. What is the ratio of the de Broglie wavelengths of the electron in the ground state to that in the excited state?

✅ Correct Answer: 1 / 4

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🧠 Concept Explanation:

In Bohr’s model: r ∝ n² (radius increases with square of energy level)
de Broglie wavelength: λ = h / mv
For electrons in orbit: λ = 2πr / n
Thus, λ ∝ n
So, λ₁ / λ₄ = 1 / 4

📌 Why This Question Matters

This problem highlights the integration of Bohr’s theory and wave mechanics. Questions like this are common in JEE Mains Physics 2025 and test both formula memorization and conceptual understanding.

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