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If the uncertainty in velocity and position of a minute particle in space are, 2.4 × 10^-²⁶(ms^-¹) and 10^-⁷(m) respectively. The mass of the particle in g is __________.

(Given: h = 6.626 × 10^-³⁴g)

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alok kumar singh | Contributor-Level 10

2 months ago

$Δ V = 2.4 \times 1 0^{- 26} m / s e c$

And $Δ x = 1 0^{- 7} m$

According to Heisenberg’s uncertainty

$Δ v \times Δ x = \frac{h}{4 π \times m}$

$∴ m = \frac{h}{4 π \times Δ v \times Δ x} = \frac{6.626 \times 1 0^{- 34}}{4 \times 3.14 \times 2.4 \times 1 0^{- 26} \times 1 0^{- 7}}$

$∴$ m = 0.02198 Kg

Or 21.98 gm

Or 22 gm in the nearest integer.

<!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1815380280"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <mi>Δ</mi> <mi>V</mi> <mo>=</mo> <mn>2</mn> <mo>.</mo> <mn>4</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>2</mn> <mn>6</mn> </mrow> </msup> <mi>m</mi> <mo>/</mo> <mi>s</mi> <mi>e</mi> <mi>c</mi> </mrow> </math> And <math> <mrow> <mi>Δ</mi> <mi>x</mi> <mo>=</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>7</mn> </mrow> </msup> <mi>m</mi> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1815380281"> </o:OLEObject></xml><! [endif]-> According to Heisenberg’s uncertainty <math> <mrow> <mi>Δ</mi> <mi>v</mi> <mo>×</mo> <mi>Δ</mi> <mi>x</mi> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <mo>×</mo> <mi>m</mi> </mrow> </mfrac> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1815380282"> </o:OLEObject></xml><! [endif]->  <math> <mrow> <mo>∴</mo> <mi>m</mi> <mo>=</mo> <mfrac> <mrow> <mi>h</mi> </mrow> <mrow> <mn>4</mn> <mi>π</mi> <mo>×</mo> <mi>Δ</mi> <mi>v</mi> <mo>×</mo> <mi>Δ</mi> <mi>x</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>6</mn> <mo>.</mo> <mn>6</mn> <mn>2</mn> <mn>6</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> <mn>4</mn> </mrow> </msup> </mrow> <mrow> <mn>4</mn> <mo>×</mo> <mn>3</mn> <mo>.</mo> <mn>1</mn> <mn>4</mn> <mo>×</mo> <mn>2</mn> <mo>.</mo> <mn>4</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>2</mn> <mn>6</mn> </mrow> </msup> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>7</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </math> <math> <mrow> <mo>∴</mo> </mrow> </math> <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1815380284"> </o:OLEObject></xml><! [endif]-> m = 0.02198 KgOr 21.98 gmOr 22 gm in the nearest integer.

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If the uncertainty in velocity and position of a minute particle in space are, 2.4 × 10^-²⁶(ms^-¹) and 10^-⁷(m) respectively. The mass of the particle in g is __________.

(Given: h = 6.626 × 10^-³⁴g)

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If the uncertainty in velocity and position of a minute particle in space are, 2.4 × 10-26(ms-1) and 10-7(m) respectively. The mass of the particle in g is __________. (Given: h = 6.626 × 10-34g)

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If the uncertainty in velocity and position of a minute particle in space are, 2.4 × 10^-²⁶(ms^-¹) and 10^-⁷(m) respectively. The mass of the particle in g is __________.

(Given: h = 6.626 × 10^-³⁴g)