completes four cycles in its orbit around the nucleus, and so represents an electron in the
n = 4 energy state.
The de Broglie wavelength, then, serves to explain why electrons can orbit the nucleus
only at certain radii.
EXAMPLE
Which of the following explains why no one has ever managed to observe and measure a de
Broglie wavelength of the Earth?
(A)The Earth is traveling too slowly. It would only have an observable de Broglie
wavelength if it were moving at near light speed.
(B) The Earth is too massive. Only objects of very small mass have noticeable wavelengths.
(C) The Earth has no de Broglie wavelength. Only objects on the atomic level have
wavelengths associated with them.
(D)“Wavelength” is only a theoretical term in reference to matter. There is no observable
effect associated with wavelength.
(E) The individual atoms that constitute the Earth all have different wavelengths that
destructively interfere and cancel each other out. As a result, the net wavelength of the
Earth is zero.This is the sort of question you’re most likely to find regarding quantum physics on SAT
II Physics: the test writers want to make sure you understand the theoretical principles
that underlie the difficult concepts in this area. The answer to this question is B. As we
discussed above, the wavelength of an object is given by the formula = h/mv. Since h is
such a small number, mv must also be very small if an object is going to have a noticeable
wavelength. Contrary to A, the object must be moving relatively slowly, and must have a
very small mass. The Earth weighs kg, which is anything but a small mass. In
fact, the de Broglie wavelength for the Earth is m, which is about as small a
value as you will find in this book.
Heisenberg’s Uncertainty Principle
In 1927, a young physicist named Werner Heisenberg proposed a counterintuitive and
startling theory: the more precisely we measure the position of a particle, the less
precisely we can measure the momentum of that particle. This principle can be expressed
mathematically as: