The de - Broglie wavelength associated with the electron in the n = 4 level is: (a) two times the de-Broglie wavelength of the electron in the ground state (b) four times the de -Broglie wavelength of the electron in the ground state (c) half of the de-Broglie wavelength of the electron in the ground state (d) 1/4th of the de-Broglie wavelength of the electron in the ground state

Answer: (b). λ = h/mv with v ∝ 1/n, so λ ∝ n. λ₄ = 4λ₁ So the answer is (b) four times the ground-state wavelength.

The de - Broglie wavelength associated with the electron in the n = 4… | JEE Main 2015 (11 Apr, Shift 1)

Q110JEE Main 2015 · 11 APR · SHIFT 1Easy

Bohr Model: Orbits, Speed & Angular Momentum

The de - Broglie wavelength associated with the electron in the n = 4 level is:

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Answer: (b)

$\lambda = \frac{h}{mv}$ with $v \propto \frac{1}{n}$ , so $\lambda \propto n$ .
$\lambda_4 = 4\lambda_1$
So the answer is (b) four times the ground-state wavelength.