## Sunday, February 20, 2011

### Mastering Physics: De Broglie Waves in the Bohr Model

The hypothesis that was put forward by Louis de Broglie in 1924 was astonishing for a number of reasons. An obvious reason is that associating a wavelike nature with particles is far from intuitive, but another astonishing aspect was how well the hypothesis fit in with certain parts of existing physics. In this problem, we explore the correspondence between the de Broglie picture of the wave nature of electrons and the Bohr model of the hydrogen atom.

Part A What is the de Broglie wavelength of the electron in the first Bohr energy level of the hydrogen atom?
Express your answer in terms of , , the mass of the electron , and the magnitude of the charge on the electron .
 =

Part B
What is the cirumference of the first () energy level in hydrogen predicted by the Bohr model of the atom?
Express your answer in terms of , , , and .
 =

Part C What is the de Broglie wavelength of the electron in the third () Bohr energy level of the hydrogen atom?
Express your answer in terms of , , , and .
 =

Part D
What is the circumference of the third () energy level in hydrogen predicted by the Bohr model of the atom?
Express your answer in terms of , , , and .