In the Bohr model of hydrogen, what is the ratio of the de Broglie wavelength of the electron in the n = 4 state to the wavelength in the n = 1 state?

Question

Quizplus · Accepted Answer

According to the de Broglie wavelength equation, λ = h/p, where h is Planck's constant and p is the momentum of the particle. In the Bohr model, the momentum of the electron is quantized and given by p = mv = nh/2πr, where m is the mass of the electron, v is its velocity, r is the radius of the orbit, and n is the principal quantum number. Thus, the de Broglie wavelength is proportional to 1/n. Therefore, the ratio of the wavelengths for n = 4 and n = 1 is (1/4)/(1/1) = 1/4 = 0.25. However, the question asks for the ratio of the de Broglie wavelengths, not the wavelengths themselves. Since both wavelengths involve h, they cancel out in the ratio and we are left with the ratio of n values, which is 4/1 = 4. Hence, the answer is C.

In the Bohr Model of Hydrogen, What Is the Ratio