just wanted to know if this is a correct substitution,
we are given kinetic energy, and want the debroglie wavelength, that eq is lamba = h / p.
= h/ mv
Momentum in terms of KE:
1/2 m (p/m)^2
1/2 m p^2/m^2
KE = p^2/2m
so...
mv can be substituted as squareroot (2*m*KE) in the h/mv eq making it h/(2*m*KE)^1/2 ?
Yes, your substitution is correct.
To find the De Broglie wavelength (λ) using kinetic energy (KE), we can use the equation λ = h/p, where h is the Planck constant and p is the momentum.
First, let's express momentum in terms of kinetic energy.
The formula for the kinetic energy is KE = p^2 / (2m), where m is the mass.
Rearranging this equation to solve for p, we get p = √(2mKE).
So, we can substitute mv with √(2mKE) in the equation λ = h/p.
That gives us λ = h / √(2mKE), which can be simplified as λ = h / (2mKE)^(1/2).
Therefore, your substitution h / (2mKE)^(1/2) is correct to determine the De Broglie wavelength given the kinetic energy.