Atomic Structure Question 511
Question: According to Heisenberg-s uncertainty principle, the product of uncertainties in position and velocities for an electron of mass $ 9.1\times {10^{-31}}kg $ is
Options:
A) $ 2.8\times {10^{-3}}m^{2}{s^{-1}} $
B) $ 3.8\times {10^{-5}}m^{2}{s^{-1}} $
C) $ 5.8\times {10^{-5}}m^{2}{s^{-1}} $
D) $ 6.8\times {10^{-6}}m^{2}{s^{-1}} $
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Answer:
Correct Answer: C
Solution:
Given that mass of electron $ =9.1\times {10^{-31}}kg $ Planck-s constant $ =6.63\times {10^{-34}}kg,m^{2}{s^{-1}} $ By using $ \Delta x\times \Delta p=\frac{h}{4\pi } $ ; $ \Delta x\times \Delta v\times m=\frac{h}{4\pi } $ where : $ \Delta x $ = uncertainity in position $ \Delta v $ = uncertainity in velocity $ \Delta x\times \Delta v=\frac{h}{4\pi \times m} $
$ =\frac{6.63\times {10^{-34}}}{4\times 3.14\times 9.1\times {10^{-31}}} $
$ =5.8\times {10^{-5}}m^{2}{s^{-1}} $ .
