Question

If alpha, beta and gamma rays carry the same momentum, which has the longest wavelength?

• A. Alpha rays
• B. Beta rays
• C. Gamma rays
• D. None, all have the same wavelength

Answer 1

Answer: (D)

On the basis of dual nature of light, de-Broglie suggested that the dual nature is not only of light, but each moving material particle has the dual nature. He assumed a wave to be associated with each moving material particle which is called the matter-wave. The wavelength of this wave is determined by the momentum of the particle. If $p$ is the momentum of the particle, the wavelength of the wave associated with it is
$\lambda =\frac{h}{p}$ , where $h$ is Planck's constant.
Since, it is given that, alpha, beta and gamma rays carry the same momentum, so they will have the same wavelength.