A proton is accelerated to 1/10th of the velocity of light. If its velocity can be measured with a precision of `+- 0.5%`, what must be its uncertanity in position?

Explanation

To solve the problem of finding the uncertainty in position of a proton accelerated to 1/10th of the velocity of light, we will use the Heisenberg Uncertainty Principle. Here’s a step-by-step solution:

### Step 1: Determine the velocity of the proton
The speed of light (c) is approximately \(3 \times 10^8\) m/s. Therefore, the velocity (v) of the proton when accelerated to \( \frac{1}{10} \) of the speed of light is:
\[ v = \frac{1}{10} \times 3 \times 10^8 \text{ m/s} = 3 \times 10^7 \text{ m/s} \]

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