Question

If an electron is travelling at $200m/s$ within $1m/s$ uncertainty, what is the theoretical uncertainty in its position in $\mu m\left(micrometer\right)$?

• A. $14.5$
• B. $29$
• C. $58$
• D. $114$

Answer 1

The correct option is C $58$

According to the Heisenberg uncertainty principle

$△x.△P\ge \frac{h}{4z}$

$△x.m_e△V\ge \frac{h}{4z}$

$△x\ge \frac{h}{4z{m}_c△V}$

$=\frac{6.626\times {10}^{-3}9}{4\times 3.14\times 9.1\times {10}^{-31}\times 1}$

$=0.058\times {10}^{-3}m=58\mu m$

So, the correct option is $C$