Frequency of the de-Broglie wave of electron in Bohr's first orbit of hydrogen atom is _____

Frequency of de-Broglie Wave in First Bohr Orbit | JEE Mains PYQ | Structure of Atom

Q. Frequency of the de-Broglie wave of electron in Bohr's first orbit of hydrogen atom is ______ × 10¹³ Hz (nearest integer).

Given:
R_H (Rydberg constant) = 2.18 × 10⁻¹⁸ J
h (Planck's constant) = 6.6 × 10⁻³⁴ J·s

Solution

Step 1: Energy of electron in first Bohr orbit

Energy of electron in nth orbit:
E_n = − R_H / n²

For first orbit (n = 1):
E₁ = − 2.18 × 10⁻¹⁸ J

Step 2: Relation between energy and frequency

Energy of matter wave:
E = hν

⇒ ν = |E| / h

Step 3: Substitute values

ν = (2.18 × 10⁻¹⁸) / (6.6 × 10⁻³⁴)

ν ≈ 0.33 × 10¹⁶ Hz
ν ≈ 3.3 × 10¹⁵ Hz

Step 4: Convert into required format

3.3 × 10¹⁵ Hz = 330 × 10¹³ Hz

Final Answer = 330

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