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jasminstg
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Using Brownian Motion to solve for 4 things PLZ HELP!
Brownian motion. Molecular motion is invisible in itself. When a small particle is suspended in a fluid, bombardment by molecules makes the particle jitter about at random. Robert Brown discovered this motion in 1827 while studying plant fertilization. Albert Einstein analyzed it in 1905 and Jean Perrin used it for an early measurement of Avogadro's number. The visible particle's average kinetic energy can be taken as , the same as that of a molecule in an ideal gas. Consider a spherical particle of density 1000 kg/m3 in water at 20°C.
(a) For a particle of diameter 35.50 µm, evaluate the rms speed.
1 __m/s
(b) The particle's actual motion is a random walk, but imagine that it moves with constant velocity equal in magnitude to its rms speed. In what time interval would it move by a distance equal to its own diameter?
2 ____ ms
(c) Repeat parts (a) and (b) for a particle of mass 71.0 kg, modeling your own body.
3 _____ m/s
4 ______ yr
(d) Find the diameter of a particle whose rms speed is equal to its own diameter divided by 3 s.
5 _____ m
(Note: You can solve all parts of this problem most efficiently by first finding a symbolic relationship between the particle size and its rms speed.)
Brownian motion. Molecular motion is invisible in itself. When a small particle is suspended in a fluid, bombardment by molecules makes the particle jitter about at random. Robert Brown discovered this motion in 1827 while studying plant fertilization. Albert Einstein analyzed it in 1905 and Jean Perrin used it for an early measurement of Avogadro's number. The visible particle's average kinetic energy can be taken as , the same as that of a molecule in an ideal gas. Consider a spherical particle of density 1000 kg/m3 in water at 20°C.
(a) For a particle of diameter 35.50 µm, evaluate the rms speed.
1 __m/s
(b) The particle's actual motion is a random walk, but imagine that it moves with constant velocity equal in magnitude to its rms speed. In what time interval would it move by a distance equal to its own diameter?
2 ____ ms
(c) Repeat parts (a) and (b) for a particle of mass 71.0 kg, modeling your own body.
3 _____ m/s
4 ______ yr
(d) Find the diameter of a particle whose rms speed is equal to its own diameter divided by 3 s.
5 _____ m
(Note: You can solve all parts of this problem most efficiently by first finding a symbolic relationship between the particle size and its rms speed.)
