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4 years ago

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Chemistry

1 answer:

Tasya [4]4 years ago

6 0

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An atom of helium has a radius of 31. pm and the average orbital speed of the electrons in it is about 4.4x 10 m/s Calculate the

otez555 [7]

The question is incomplete, here is the complete question:

An atom of helium has a radius of 31. pm and the average orbital speed of the electrons in it is about $4.4\times 10^6m/s$ . Calculate the least possible uncertainty in a measurement of the speed of an electron in an atom of helium. Write your answer as a percentage of the average speed, and round it to 2 significant digits

Answer: The percentage of average speed is 41 %

Explanation:

We are given:

Radius of helium atom = 31 pm = $31\times 10^{-12}m$ (Conversion factor: $1m=10^{12}pm$ )

So, diameter of helium atom = $(2\times r)=(2\times 31\times 10^{-12})=64\times 10^{-12}m$

The diameter of the atom will be equal to the uncertainty in position.

The equation representing Heisenberg's uncertainty principle follows:

$\Delta x.\Delta p=\frac{h}{2\pi}$

where,

$\Delta x$ = uncertainty in position = d = $64\times 10^{-12}m$

$\Delta p$ = uncertainty in momentum = $m\Delta v$

m = mass of electron = $9.1095\times 10^{-31}kg$

h = Planck's constant = $6.627\times 10^{-34}kgm^2/s^2$

Putting values in above equation, we get:

$64\times 10^{-12}m\times 9.1095\times 10^{-31}kg\times \Delta v=\frac{6.627\times 10^{-34}kgm^2/s}{2\times 3.14}\\\\\Delta v=\frac{6.627\times 10^{-34}kgm^2/s^2}{2\times 3.14\times 64\times 10^{-12}m\times 9.1095\times 10^{-31}kg}=1.81\times 10^6m/s$

To calculate the percentage of average speed, we use the equation:

$\text{Percentage of the average speed}=\frac{\text{Uncertainty in velocity}}{\text{Average orbital speed}}\times 100$

We are given:

Average orbital speed = $4.4\times 10^6m/s$

Putting values in above equation, we get:

$\text{Percentage of the average speed}=\frac{1.81\times 10^6m/s}{4.4\times 10^6m/s}\times 100\\\\\text{Percentage of the average speed}=41.\%$

Hence, the percentage of average speed is 41 %

3 0

4 years ago

If the copper is drawn into wire whose diameter is 9.50 mm, how many feet of copper can be obtained from the ingot? The density

ankoles [38]

Answer:

The length of the wire = 352.66 feet.

Explanation:

A copper refinery produces a copper ingot weighing 150 lb. If the copper is drawn into wire whose diameter is 9.50 mm, how many feet of copper can be obtained from the ingot? The density of copper is 8.94 g/cm3. (Assume that the wire is a cylinder whose volume is V = πr2h, where r is the radius and h is its height or length.)

Step 1: Convert lb to kg

150 lb = 68.0389 kg

Step 2: Calculate volume of copper

Volume = mass / density

Volume = 68038.9 grams / 8.94 g/cm³

Volume = 7610.6 cm³ Cu

Step 3: Calculate length of wire

The diameter of the wire is 9.50 mm, so the radius is half of that (4.75 mm), or 0.475 cm.

The total "volume" of the wire is πr²h = (π)*(0.475 cm)²(h) = 0.708h = 7610 cm^3

7610 = 0.708h

h = 10749 cm = length of wire

The length of the wire = 352.66 feet.

7 0

4 years ago

Which of the following statements holds true for a chemical change?

sp2606 [1]

A chemical change creates a new substance

5 0

4 years ago

Hammer orchids are plants with flowers that are highly modified to resemble a female thynnid wasp (i.e., a wasp of the Thynnidae

nlexa [21]

Answer:

study

Explanation:

you wouldn't be asking this question if you study

7 0

4 years ago

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How many feet are in 6.75 miles? (6.75x1) divided by 5280 =

disa [49]

Answer:

0.00127840909

Explanation:

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7 0

3 years ago