Question

A ball has a mass of 90 g and speed of 45 m/s. If speed can be measured with accuracy of 2%, then calculate uncertainty in position.
Please tell how to do this question. I have an exam tomorrow, so please don’t scam…

Answer 1

Explanation:

ye 90 g hai ya 40 g maina apko 40g ke hisab sab sa kar ka dhika rahi hu koi baat nhi ap issa 40 g ka waja 90 g laga da na

Q A ball has a mass of 40 g and speed of 45 m/s. If speed can be measured with accuracy of 2%, then calculate uncertainty in position.

solution

Use Heisenberg's uncertainty principle.

For example [Δx=4πmΔvh]

Here,  Δx  is the uncertainty in the position.

Δv is the uncertainty in velocity

m is the mass of Particle.

Given,m=40g=0.04kg

Δv=2%ofv=2×10045=0.9m/s

h=6.626×10−34J.s

Now,Δx=(4×3.14×0.04×0.9)6.626×10−34

=1.4654×10−33m. Ans

With Another Method

Solution

Using heisenberg's uncertainty principle,

      Δ=h/4πmΔv

      Δx = uncertainty in position

Δv=2%ofv=2×45/100=0.9 m/s

now Δx=(4×3.14×0.04×0.9)6.626×10−34

 =1.46×10−33 m. Ans

Answer 2

Explanation:

Using Heisenberg uncertainty principle

$px \geqslant \frac{h}{4\pi}$

Where 'p' is uncertainty in momentum and 'x' is uncertainty in position.

Using the definition of momentum,

$p = mv$

Where v is uncertainty in speed.

So using the equality we have,

$mvx = \frac{h}{4\pi}$

$x = \frac{h}{4\pi \times mv}$

Now , 2% accuracy in speed means

$v = 0.02 \times 45 = 0.9 \\ mv = 81 \times {10}^{ - 3}$

Here we used mass in kg

so,

$x = \frac{h}{4\pi \times 81 \times {10}^{ - 3} }$

This is the uncertainty in position with 'h' as the planck's constant

$h = 6.63 \times {10}^{ - 34}$