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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
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B
7.68cm
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C
0.175cm
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D
3.84cm
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Solution

The correct option is C $$0.175cm$$
velocity $$V=3\times 10^4\ cm/s$$
uncertainty in velocity $$\triangle v = 3 \times 10^4\times \dfrac{0.011}{100}=3.3\ cm/s$$   
Heisenberg uncertainty principal 
$$\triangle p. \triangle x \ge \dfrac{h}{4z}$$
$$m\triangle v \triangle x \ge \dfrac{h}{4z}$$
$$\triangle x \ge \dfrac{h}{4zm\triangle v}$$
$$\triangle x \ge \dfrac{6.626\times 10^{-27}}{4\times 3.14\times 9.1\times 10^{-28}\times 3.3}$$
$$0.175\ cm$$























Chemistry

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