Question

the mass of a particle is 10^-10g if its velocity is 10^-6 with 0.00001% uncertainty in measurement the uncertainty in position is​

Answer 1

hey look in the qstion there is this line given as velocity with 0.00001%uncertainity. It means the delVwill be 0.00001% of 10^-6. Thats why ur answer is not coming. here is ur soln...hope it helps u"!

Answer 2

Given:

Mass of the particle = 10¹⁰g

Velocity = 10⁻⁶ cms⁻¹

Uncertainty in velocity = 0.00001%

To find:

Uncertainty in position

Solution:

The formula of Heisenberg Uncertainty principle is being used in this-

It states that for a microscopic particle it is impossible to calculate the accurate position and velocity on the same time.

It's formula is -

    Δx.Δp = $\frac{h}{4\pi }$

here, Δx = uncertainty in position

        Δp = uncertainty in velocity

           h = Planck's constant

         4π = constant

it is given,  

     v = 10⁻⁶ cm/s

     Δv = 0.00001% of v

     Δv = $\frac{1}{100000} \times 10^-^6$ × 10⁻²

    Δv = 10⁻⁶⁻⁵⁻²

    Δv = 10⁻¹³

now, find Δp, we find

   Δp = mΔv

here, m = mass of a particle

         Δv = uncertainty in velocity

putting values of m and v, we get

    Δp = mΔv = 10⁻¹⁰ × 10⁻¹³

            Δp = 10⁻²³

        h = 6.626 × 10⁻³⁴m²kgs⁻¹

So, putting all the values, we get

     Δx.Δp = $\frac{h}{4\pi }$

      $\Delta x = \frac{6.626 \times 10^-^3^4}{4 \times 3.14 \times 10^-^2^3}$

      Δx = 0.527 × 10⁻³⁴⁺²³

      Δx = 0.527 × 10⁻¹¹

Therefore, the uncertainty in position is 0.527 × 10⁻¹¹.