Question

Calculate the uncertainty in the momentum of an electron if it is confined to a linear region of length $1\times {10}^{-10}$ metre.

• A. $5.37\times {10}^{-27}kgm{s}^{-1}$
• B. $5.27\times {10}^{-27}gm{s}^{-1}$
• C. $5.37\times {10}^{-25}gm{s}^{-1}$
• D. $5.27\times {10}^{-25}gm{s}^{-1}$

Answer 1

Answer: (D)

$5.27\times {10}^{-25}gm{s}^{-1}$

Answer:-

According to Heisenberg's uncertainty principle,

$\Delta x\Delta p\ge \frac{h}{4\pi }$

Where $\Delta x\&\Delta p$ are the uncertainty in position and momentum respectively and h is Planck’s Constant.

Now, the uncertainty in position here is simply the region where your electron is confined. Here, it is ${10}^{-10}$

$\therefore \Delta p\ge \frac{h}{4\pi \times \Delta x}$

$\Rightarrow \Delta p\ge \frac{6.63\times {10}^{-34}}{4\times 3.14\times {10}^{-10}}$

$\Rightarrow \Delta p\ge 5.27\times {10}^{-25}gm{s}^{-1}$

Hence, the uncertainty in the momentum is $5.27\times {10}^{-25}gm{s}^{-1}$