Atomic Structure Question 379
Question: In an atom, an electron is moving with a speed of 600 m/s with an accuracy of 0.005%. Certainity with which the position of the electron can be located is ( $ h=6.6\times {10^{-34}}kg,m^{2}{s^{-1}} $ , mass of electron, $ e_{m}=9.1\times {10^{-31}}kg $ )
Options:
A) $ 5.10\times {10^{-3}}m $
B) $ 1.92\times {10^{-3}}m $
C) $ 3.84\times {10^{-3}}m $
D) $ 1.52\times {10^{-4}}m $
Show Answer
Answer:
Correct Answer: B
Solution:
- According to Heisenberg uncertainty principle. $ \Delta x.m\Delta v=\frac{h}{4\pi } $
$ \Delta x=\frac{h}{4\pi m\Delta v} $ Here $ \Delta v=\frac{600\times 0.005}{100}=0.03 $ So, $ \Delta x=\frac{6.6\times {10^{-34}}}{4\times 3.14\times 9.1\times {10^{-31}}\times 0.03} $
$ =1.92\times {10^{-3}} $
