Question
Find the de-Broglie wavelengths of (a) a 46-g golf ball with a velocity of 30 m/s, and (b) an electron with a velocity of 107 m/s.
Solution
(a) For a golf ball,
Since Velocity of wave < < speed of light, we can let m = m0.
This is the relativistic mass.
Hence,
The wavelength of the golf ball is so small as compared with its dimensions that we would not expect to find any wave aspects in its behaviour.
(b) For an electron,
Again V < < c, so with m = m0 = 9.1 x 10–31 kg,
We have,
De-broglie wavelength assosciated with the electron,
The dimensions of electron is comparable with this figure—the radius of the hydrogen atom, for instance is 5.3 x 10–11 m.
It is therefore not surprising that the wave character of moving electrons is the key to understanding atomic structure and behaviour.
Since Velocity of wave < < speed of light, we can let m = m0.
This is the relativistic mass.
Hence,
The wavelength of the golf ball is so small as compared with its dimensions that we would not expect to find any wave aspects in its behaviour.
(b) For an electron,
Again V < < c, so with m = m0 = 9.1 x 10–31 kg,
We have,
De-broglie wavelength assosciated with the electron,
The dimensions of electron is comparable with this figure—the radius of the hydrogen atom, for instance is 5.3 x 10–11 m.
It is therefore not surprising that the wave character of moving electrons is the key to understanding atomic structure and behaviour.
