KVPY Sample Paper KVPY Stream-SX Model Paper-2

Uncertainty in position of an electron \[(mass\text{ }=9.1\times {{10}^{-28}}g)\] moving with a velocity \[3\times {{10}^{4}}\,cm/s,\] accurate up to \[0.001%,\] will be: \[(h\text{ }=\text{ }6.626\times \text{ 1}{{\text{0}}^{-27}}\])

A) \[1.93cm\]

B) \[3.84cm\]

C) \[5.76cm\]

D) \[7.68cm\]

Correct Answer: A

Solution :

[a]

Given mass of an electron (m) \[=9.1\times {{10}^{-28}}g;\]

Velocity of electron (v) \[=3\times {{10}^{4}}cm/s\]

Accuracy in velocity \[=0.001%=\frac{0.001}{100}\]

Actual velocity of the electron\[(\Delta x)=3\times {{10}^{4}}\times \frac{0.0001}{100}=0.3cm/s\]

Planck?s constant (h)\[=6.626\times {{10}^{-27}}erg-\sec .\]

\[\therefore \]Uncertainty in the position of the electron \[(\Delta x)=\frac{h}{4\pi m\Delta v}\]

\[=\frac{6.626\times {{10}^{-27}}\times 7}{4\times 22\times \left( 9.1\times {{10}^{-28}} \right)\times 0.3}\]

\[=1.93cm\]