Problem

Problem

In the Bohr model of the hydrogen atom, what is the de-Broglie wavelength for the electron when it is in (a) the n=1n = 1 level? (b) the n=4n = 4 level? In each case, compare the de-Broglie wavelength to the circumference 2πrn2\pi r_n of the orbit.
Intuitive explanation

The de Broglie wavelength connects the particle nature of the electron to its wave nature through λ=h/p\lambda = h/p, where pp is momentum. In the Bohr model, the electron orbits at specific energy levels, each with a definite velocity and radius—so you'll need to find the electron's momentum at that level using the Bohr radius and the relationship between orbital velocity and the principal quantum number. Once you have momentum, the wavelength follows directly.

Intuitive explanation

The de Broglie wavelength connects the particle nature of the electron to its wave nature through λ=h/p\lambda = h/p, where pp is momentum. In the Bohr model, the electron orbits at specific energy levels, each with a definite velocity and radius—so you'll need to find the electron's momentum at that level using the Bohr radius and the relationship between orbital velocity and the principal quantum number. Once you have momentum, the wavelength follows directly.

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