Question

The uncertainty in the position of an electron $(mass=9.1\times {10}^{-28}g)$ moving with a velocity of $3.0\times {10}^4{cm}^{-1}$ accurate up to $0.011\%$, will be:

• A. $1.92cm$
• B. $7.68cm$
• C. $0.175cm$
• D. $3.84cm$

Answer 1

The correct option is C $0.175cm$

velocity $V=3\times {10}^{4}cm/s$

uncertainty in velocity $△v=3\times {10}^4\times \frac{0.011}{100}=3.3cm/s$

Heisenberg uncertainty principal

$△p.△x\ge \frac{h}{4z}$

$m△v△x\ge \frac{h}{4z}$

$△x\ge \frac{h}{4zm△v}$

$△x\ge \frac{6.626\times {10}^{-27}}{4\times 3.14\times 9.1\times {10}^{-28}\times 3.3}$

$0.175cm$