Question

The de-Broglie wavelength of a particle of mass 6.63 g moving with a velocity of 100 m/s is:
$
  {\text{A}}{\text{. 1}}{{\text{0}}^{ - 33}}m \\
  {\text{B}}{\text{. 1}}{{\text{0}}^{ - 35}}m \\
  {\text{C}}{\text{. 1}}{{\text{0}}^{ - 31}}m \\
  {\text{D}}{\text{. 1}}{{\text{0}}^{ - 25}}m \\
$

Answer 1

Hint: The De-Broglie wavelength of a particle is equal to the Planck’s constant divided by the momentum of the particle. The momentum of a particle is equal to the product of its mass and the velocity. Using given information in this formula, we can obtain the required solution.

Formula used:
The de-Broglie wavelength of particle of mass m and having velocity v is given as
$\lambda = \dfrac{h}{p} = \dfrac{h}{{mv}}$

Complete answer:
We are given a particle whose mass is given as
$m = 6.63g = 6.63 \times {10^{ - 3}}kg$
This particle is travelling with a velocity v whose value is given as
$v = 100m/s$
We know the formula for the de-Broglie wavelength of a particle which is given as
$\lambda = \dfrac{h}{p} = \dfrac{h}{{mv}}$
Here p represents the momentum of the given particle which is equal to the product of the mass and the velocity of the given particle; h is known as the Planck’s constant whose value is given as
$h = 6.626 \times {10^{ - 34}}Js$
Now we can directly substitute these values into the formula for the de-Broglie wavelength of the given particle. Doing so, we get
$\lambda = \dfrac{{6.63 \times {{10}^{ - 34}}}}{{6.63 \times {{10}^{ - 3}} \times 100}} = {10^{ - 33}}m$
This is the required value of the de-Broglie wavelength of the given particle.

Hence, the correct answer is option A.

Additional information:
De-Broglie postulated that with every matter particle, there is a wavelength associated called the de-Broglie wavelength. It plays a significant role when we measure it for subatomic particles in the quantum regime.

Note:
1. All units should be in the same system of units.
2. It should be noted that the de-Broglie wavelength obtained for the given particle is very small. It depends on the mass of the particle and its velocity. Larger the values of the mass and/or the velocity of the given particle, smaller is the obtained de-Broglie wavelength.