Question

Paramecium wavelength.

A paramecium is covered with motile hair called cilia that propel it at a speed of 1mm/s.
PartA: if the paramecium has a volume of 2E-13m3 and a density equal that of water, what is the de brogile wavelength when in motion?
Part B: what fraction of the paramecium 150um in length does this wavelength represent?
Please explain step by step instructions for this problem.
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Answer #1
e = mc^2 = hf = hc/L we have L = hc/mc^2 = h/mc for the dB wave.

The little guy's rest mass m = Rho V = 1000 * 2E-13 = ? kg. Look up c, light speed, as precise as you can find and, h, Planck's Constant, and plug in m inL = h/mc. Rho = 1000 kg/m^3 is fresh water density. You can do the math.

Then l/L = e = ? the fraction of the little bug's length (l = 150E-6 m) to the DB length.
answered by: HeythereDeliah
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Answer #2

Part A)

We can first find the mass of the paramecium using the formula ρ = m/V

The density of water is 1000 kg/m3, so...

1000 = (m)/(2 X 10-13)

m = 2 X 10-10 kg

The formula for deBroglie wavelength is

λ = h/mv

v is 1 mm/s which is 1 X 10-3 m/s

λ = (6.63 X 10-34)/(2 X 10-10)(1 X 10-3)

λ = 3.315 X 10-21 m

Part B)

The fraction can be calculated as 3.315 X 10-21/150 X 10-6

That is 2.21 X 10-17

answered by: Jimmy S
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Answer #3

The speed of parameciumis 1 mm/ -1x103 m/s The volume of paramecium isび-2x10-15 m Density of paramecium is p-1000 kg/m The ma

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Answer #4

Part A)

We can first find the mass of the paramecium using the formula ρ = m/V

The density of water is 1000 kg/m3, so...

1000 = (m)/(2 X 10-13)

m = 2 X 10-10 kg

The formula for deBroglie wavelength is

λ = h/mv

v is 1 mm/s which is 1 X 10-3 m/s

λ = (6.63 X 10-34)/(2 X 10-10)(1 X 10-3)

λ = 3.315 X 10-21 m

Part B)

The fraction can be calculated as 3.315 X 10-21/150 X 10-6

That is 2.21 X 10-17

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Answer #5
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