Question

If the momentum of a particle is doubled, what happens to its de Broglie wavelength?

it decreases by a factor of 2^-1/2

it doubles

it halves

it becomes slightly less than half

it slightly more than doubles

Answer 1

Ans: it halves

Because According to formula of de Broglie wavelength - wavelength is inversly proportional to momentum.

In some situations, light behaves like a wave, while in others, it behaves like particles. The particles of light are called photons, and they can be thought of as both waves and particles. Louis de Broglie developed a formula to relate this dual wave and particle behavior. It can also be applied to other particles, like electrons and protons. The formula relates the wavelength to the momentum of a wave/particle.

For particles with mass (electrons, protons, etc., but not photons), there is another form of the de Broglie wavelength formula. At non-relativistic speeds, the momentum of a particle is equal to its rest mass, m, multiplied by its velocity, v.

The unit of the de Broglie wavelength is meters (m), though it is often very small, and so expressed in nanometers (1 nm = 10^(-9) m), or Angstroms ().

λ = the de Broglie wavelength (m)

h = Planck's constant ()

p = momentum of a particle ()

m = mass of a particle (kg)

v = velocity of a particle (m/s)