Let's assume you use green light (λ = 550 nm) to look at an electron. What is the uncertainty in determining the electron's velocity? Express your answer rounded up to the nearest hundredth.
To determine the uncertainty in determining the electron's velocity, we can use Heisenberg's uncertainty principle. According to this principle, the uncertainty in the position (Δx) and momentum (Δp) of a particle are related by the equation:
Δx * Δp >= h/4π,
where h is the Planck's constant (6.626 x 10^-34 J·s).
In this case, we want to find the uncertainty in the electron's velocity, which is related to momentum (p) by the equation:
p = mv,
where m is the mass of the electron and v is its velocity.
The uncertainty in momentum (Δp) can be calculated using the uncertainty in wavelength (Δλ) due to the diffraction of light. The uncertainty in wavelength can be determined using the equation:
Δλ >= λ^2 / (2d),
where d is the width of the slit or aperture through which the light passes.
Since we are using green light with a wavelength of λ = 550 nm, we can substitute this value into the equation to find the value of Δλ.
Next, we can calculate the uncertainty in momentum (Δp) using the formula:
Δp = h / (2πΔλ).
Finally, to find the uncertainty in velocity (Δv), we can divide the uncertainty in momentum (Δp) by the mass of the electron (m).
Δv = Δp / m.
By following these steps and plugging in the values, you can calculate the uncertainty in determining the electron's velocity.