PhysicsNEET 2025Matter waves and de Broglie wavelength

Dual Nature of Radiation and Matter

The de Broglie wavelength of an electron orbiting in the $n = 2$ state of the hydrogen atom is close to (given Bohr radius = 0.052 nm):

A.0.067 nm
B.0.67 nm✓
C.1.67 nm
D.2.67 nm

Solution

In the $n$ th orbit the circumference equals $n$ de Broglie wavelengths: $2 π r_{n} = nλ$ . With $r_{2} = 4 a_{0} = 0.208$ nm: $λ = \frac{2 π \times 0.208}{2} \approx 0.65$ nm $\approx 0.67$ nm.

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Dual Nature of Radiation and Matter

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