Light with wavelength 5.6 * 10^-7 is used to determine the position of an electron to within the wavelength of the light.What is the resulting uncertainty in the electron's velocity? h = 6.63 *10^-34 J.s,m_e = 9.11 * 10^-31 kg A)1300 m/s B)103 m/s C)207 m/s D)16,331 m/s

Question

Quizplus · Accepted Answer

The uncertainty principle states that ΔxΔp ≥ h/4π, where Δx is the uncertainty in position and Δp is the uncertainty in momentum. We know that Δx = wavelength of light = 5.6 x 10^-7 m. To find Δp, we can use the equation p = mv, where m is the mass of the electron and v is its velocity. Rearranging, we get v = p/m. We want to find the uncertainty in velocity, so we need to find Δv.

From the equation ΔxΔp ≥ h/4π, we can solve for Δp: 
Δp ≥ h/(4πΔx) 
Δp ≥ (6.63 x 10^-34 J s)/(4π x 5.6 x 10^-7 m) 
Δp ≥ 2.37 x 10^-27 kg m/s

Now we can find Δv: 
Δv = Δp/m 
Δv = (2.37 x 10^-27 kg m/s)/(9.11 x 10^-31 kg) 
Δv = 260.5 m/s

Therefore, the resulting uncertainty in the electron's velocity is approximately 260 m/s. The closest answer choice is B, 103 m/s.

​Light with Wavelength 5

Light with Wavelength 5