Question

as per de- broglie formula ,a macroscopic particle of mass 100g moves with a velocity 100 cm s-1 calculate the wave length​

Answer 1

Explanation:

Write the de Broglie equation and establish a relation between wavelength of a moving

subatomic particle and its kinetic energy.

Answer 2

Given :

Mass of particle = 100g = 0.1kg

Velocity = 100 cm/s = 1 m/s

To Find :

de Broglie wavelength associated with the macroscopic particle.

Solution :

❒ Wavelength associated with any moving microscopic or macroscopic particle is inversely proportional to the momentum.

• Momentum is measured as the product of mass and velocity.

de Boglie equation :-

$\bigstar\:\underline{\boxed{\bf{\red{\lambda=\dfrac{h}{p}=\dfrac{h}{mv}=\dfrac{h}{\sqrt{2mE_k}}=\dfrac{h}{\sqrt{2mqV}}}}}}$

• Ek denotes kinetic energy
• q denotes charge of particle
• m denotes mass
• v denotes velocity
• V denotes accelerating potential
• h denotes plank's constant

By substituting the given values;

$\sf:\implies\:\lambda=\dfrac{6.6\times 10^{-34}}{(0.1)(1)}$

$\sf:\implies\:\lambda=(6.6\times10^{-34})\times 10$

$:\implies\:\underline{\boxed{\bf{\purple{\lambda=6.6\times 10^{-33}\:m}}}}$