calculate the momentum of a particle ,whose de Broglie's wave length is 0.1nm ?
To calculate the momentum of a particle using its de Broglie wavelength, you can use the de Broglie equation, which relates the wavelength (λ) of a particle to its momentum (p):
λ = h / p,
where:
- λ is the de Broglie wavelength,
- h is the Planck's constant (h = 6.626 × 10^-34 J·s), and
- p is the momentum of the particle.
Given that the de Broglie wavelength (λ) is 0.1 nm, we need to convert it to meters, since the SI unit of length is meter:
0.1 nm = 0.1 × 10^-9 m = 10^-10 m.
We can now rearrange the de Broglie equation to solve for momentum (p):
p = h / λ.
Substituting the values, we get:
p = 6.626 × 10^-34 J·s / 10^-10 m.
Using basic algebra, we can simplify this equation by dividing the numerator and denominator by 10^-10:
p = (6.626 × 10^-34 J·s) / (10^-10 m / 1).
Simplifying further by multiplying the numerator and denominator by 10^10, we get:
p = (6.626 × 10^-34 J·s) × (10^10 m).
Calculating, we find:
p = 6.626 × 10^-24 J·m·s.
Therefore, the momentum of the particle is approximately 6.626 × 10^-24 J·m·s.