A particle has a velocity that is 92% of the speed of light. If the wavelength of the particle is 1.55×10-15 m, calculate the mass of the particle.
wavelength = h/mv
You have wavelength, h, and v (0.92*3E8 m/s). Calculate m.
Post your work if you get stuck.
To calculate the mass of the particle, we need to use the relativistic mass formula:
m = m0 / sqrt(1 - (v^2 / c^2))
Where:
m0 = rest mass of the particle
v = velocity of the particle
c = speed of light in a vacuum
Given:
v = 92% of the speed of light = 0.92c
wavelength (λ) = 1.55×10^(-15) m
Now, we know that the speed of light is approximately 3.00×10^8 m/s. Therefore:
c = 3.00×10^8 m/s
Let's calculate the mass of the particle using the formula:
m = m0 / sqrt(1 - (v^2 / c^2))
First, we need to find the value of v^2 / c^2:
v^2 / c^2 = (0.92c)^2 / (3.00×10^8 m/s)^2
= (0.92)^2 * (c^2 / c^2)
= 0.8464 * 1
= 0.8464
Now, substitute the value of v^2 / c^2 into the formula:
m = m0 / sqrt(1 - 0.8464)
To find the value of m, we need to know the rest mass of the particle, m0. Unfortunately, this information is missing from the given problem statement. Without the rest mass, it's not possible to calculate the mass of the particle using this formula alone.
Please provide the value of the rest mass of the particle (m0) if it is available, or any other additional information that might be relevant.