The kinetic energy of a massive particle is equal to the energy of a photon. The massive particle moves at 1.49 % the speed of light.
What is the ratio of the photon wavelength to the de Broglie wavelength of the particle? (Assume the standard nonrelativistic expressions for the momentum and kinetic energy of the massive particle.)
The deBroglie wavelength of a particle is ë=h/mv
The wavelength of a photon is ë=hc/E
Since we know that the energy 'E' of the photon is equal to the Kinetic energy of the massive particle, E=1/2mv^2.
We are also given that v is 0.0149c.
This is the ratio
hc/(1/2m(0.0149c)^2) : h/m(0.0149c)
The equivalent terms on each side of the ratio cancel, leaving...
2/(0.0149) : 1
Your answer should be 134.23
I tried this and it did not work for me
To find the ratio of the photon wavelength to the de Broglie wavelength of the particle, let's break down the problem into steps.
Step 1: Find the kinetic energy of the massive particle.
The non-relativistic expression for the kinetic energy of a particle is given by:
K = (1/2) * m * v^2
Where K is the kinetic energy, m is the mass of the particle, and v is its velocity.
Step 2: Determine the momentum of the particle.
The non-relativistic expression for the momentum of a particle is given by:
p = m * v
Where p is the momentum, m is the mass of the particle, and v is its velocity.
Step 3: Calculate the de Broglie wavelength of the particle.
The de Broglie wavelength is given by the formula:
λ = h / p
Where λ is the wavelength, h is the Planck's constant (approximately 6.626 x 10^-34 J·s), and p is the momentum.
Step 4: Calculate the energy of the photon.
The energy of a photon is given by the equation:
E = h * c / λ
Where E is the energy, h is Planck's constant, c is the speed of light (approximately 3 x 10^8 m/s), and λ is the wavelength of the photon.
Step 5: Find the ratio of photon wavelength to the de Broglie wavelength.
Ratio = λ_photon / λ_particle
Now, let's plug in the given information and calculate the ratio.
Given:
v_particle = 1.49% of the speed of light
Step 1: Find the kinetic energy of the particle.
K = (1/2) * m * v^2
Since the mass of the particle is not provided, we need more information to calculate the kinetic energy.
Therefore, without the value of the mass of the particle, it is not possible to solve the problem and determine the ratio of the photon wavelength to the de Broglie wavelength of the particle.