Find Beta and Gamma for an electron that has a kinetic energy of 6.00 keV. â?
gamma = KE/MoC^2 + 1
Beta = 1/gamma^2 + 1
gamma = 1.011723381
Beta = 1.9769592
I got gamma correct but my answer but im getting gamma incorrect can anyone explain what could be wrong
To find the correct values for gamma and beta, we need to use the correct formulas. Here is the correct process:
First, we need to know the mass of the electron, which is approximately 9.11 x 10^-31 kg. Let's denote it as "m".
The speed of light, c, is approximately 3 x 10^8 m/s.
Now, to calculate gamma, we use the equation:
gamma = KE / (mc^2) + 1
where KE is the kinetic energy.
Given that the kinetic energy is 6.00 keV, we need to convert it to joules since the units must be consistent:
1 keV = 1.6 x 10^-16 J
So, 6.00 keV = 6.00 x 1.6 x 10^-16 J = 9.6 x 10^-16 J
Plugging this value into the formula for gamma, we have:
gamma = (9.6 x 10^-16 J) / (9.11 x 10^-31 kg x (3 x 10^8 m/s)^2) + 1
gamma = 1.0109
Now, to find beta, we use the equation:
beta = sqrt(1 - (1 / gamma^2))
beta = sqrt(1 - (1 / (1.0109)^2))
beta = sqrt(1 - (1 / 1.02194))
beta = sqrt(0.97826)
beta = 0.9891
Therefore, the correct values are:
gamma = 1.0109
beta = 0.9891
Make sure to double-check your calculations and use the correct formulas when solving similar problems.