**Uncertainty in Position of an Electron**

To determine the uncertainty in the position of an electron moving with a velocity of 3 x 10^4 cm/sec accurate up to 0.011%, we can make use of the Heisenberg's Uncertainty Principle. According to this principle, there is a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position and momentum, can be known simultaneously.

**Heisenberg's Uncertainty Principle:**
The principle states that the product of the uncertainties in the position and momentum of a particle is greater than or equal to a constant value, known as Planck's constant (h), divided by 4π.

Δx * Δp ≥ h/4π

Where:
Δx = uncertainty in position
Δp = uncertainty in momentum
h = Planck's constant (6.626 x 10^-34 J.s)

**Calculating Uncertainty in Momentum:**
The momentum (p) of an electron can be calculated using the formula:

p = m * v

Where:
m = mass of the electron (9.10938356 x 10^-31 kg)
v = velocity of the electron (3 x 10^4 cm/sec)

By substituting the values into the equation, we can calculate the momentum of the electron.

p = (9.10938356 x 10^-31 kg) * (3 x 10^4 cm/sec)

**Converting Units:**
To ensure that the units are consistent, we need to convert the mass from kilograms to grams and the velocity from cm/sec to m/s.

m = 9.10938356 x 10^-31 kg = 9.10938356 x 10^-28 g
v = 3 x 10^4 cm/sec = 300 m/s

**Calculating Uncertainty in Momentum:**
Now, we can calculate the uncertainty in momentum (Δp) using the given accuracy of 0.011%.

Δp = 0.011% * p

**Converting Percent to Decimal:**
To calculate the uncertainty, we need to convert the percentage to a decimal form.

0.011% = 0.011/100 = 0.00011

**Calculating Uncertainty in Position:**
Using the Heisenberg's Uncertainty Principle equation, we can calculate the uncertainty in position (Δx).

Δx * Δp = h/4π

Δx = (h/4π) / Δp

Substituting the values, we get:

Δx = (6.626 x 10^-34 J.s) / (4π * Δp)

**Final Calculation:**
By plugging in the values, we can calculate the uncertainty in position.

Δx = (6.626 x 10^-34 J.s) / (4π * 0.00011 * p)

After substituting the values of p, we can calculate the uncertainty in position accurately.