Question

If an electron is travelling at $200m/s$ with $1m/s$ uncertainty, theoretical uncertainty in its $\mu m$ will be ?

• A. $14$
• B. $58$
• C. $70$
• D. $97$

Answer 1

The correct option is B $58$

$v=200m/s;△V=1m/s=$ uncertainity in velocity.

According to Heseinberg
Uncertainity Principle,

$△x.m△V\ge \frac{h}{4\pi }$

$△x.△V\ge \frac{h}{4\pi m}$

$△x\ge \frac{6.626\times {10}^{-34}}{4\times 3.14\times {10}^{-31}\times 9.1\times 1}$

$△x\ge 58um$

Therefore, uncertainty in position is $58um$