A 281 lb fullback runs the 40 yd dash at a speed of 23.0 ± 0.1 mi/h.(a) What is his de Broglie wavelength (in meters)?(b) What is the uncertainty in his position?
i determined the wavelength correctly, but how do you determine the uncertainty
wavelength = h/mv
± 0.1 mi/h
http://www.jiskha.com/display.cgi?id=1284677676
To determine the uncertainty in the fullback's position, you will need to use the Heisenberg uncertainty principle. The uncertainty principle states that there is a fundamental limit to how precisely we can know both the position and momentum of a particle.
The uncertainty in position (∆x) is related to the uncertainty in momentum (∆p) by the following equation:
∆x * ∆p ≥ h/4π
where h is the Planck constant (h = 6.626 x 10^-34 J·s).
In this case, the momentum (∆p) can be determined using the mass and velocity of the fullback. The uncertainty in momentum can be calculated as:
∆p = mass * ∆v
where mass is given as 281 lb (which needs to be converted to kg) and ∆v is the uncertainty in velocity.
Once you have the uncertainty in momentum (∆p), you can rearrange the equation to solve for the uncertainty in position (∆x):
∆x = (h/4π) / ∆p
Now, let's calculate the uncertainty in position:
Step 1: Convert the mass from pounds to kg.
1 lb is approximately equal to 0.453592 kg.
So, 281 lb = 281 * 0.453592 kg ≈ 127.5 kg.
Step 2: Convert the speed from miles per hour (mi/h) to meters per second (m/s).
1 mi/h is equal to approximately 0.44704 m/s.
So, 23.0 mi/h ≈ 23.0 * 0.44704 m/s ≈ 10.27 m/s.
Step 3: Calculate the uncertainty in velocity (∆v).
The uncertainty in velocity (∆v) was given as ± 0.1 mi/h.
So, in meters per second, ∆v = 0.1 * 0.44704 m/s.
Step 4: Calculate the uncertainty in momentum (∆p).
∆p = mass * ∆v = 127.5 kg * (0.1 * 0.44704 m/s).
Step 5: Calculate the uncertainty in position (∆x).
∆x = (h/4π) / ∆p = (6.626 x 10^-34 J·s / (4π)) / (∆p).
Now, plug in the values to calculate the uncertainty in position (∆x).