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6. (a)Estimate the rms speed of an amino acid whose molecular mass is `89\ u` in a living cell at `37°C`.
(b) What would be the rms speed of a protein of molecular mass `50,000\ u` at `37°C`?
6. (a)Estimate the rms speed of an amino acid whose molecular mass is 89\ u in a living cell at 37°C.
(b) What would be the rms speed of a protein of molecular mass 50,000\ u at 37°C? `v_(rms) = sqrt((2kT)/m)`
a)
`v_(rms) = 2.9 times 10^2 m//s`
b)
`v_(rms) = 12 m//s`
Given:
`T = 37°C = 310\ K`
`m_a = 89\ u = 89 times 1.66 times 10^(-27)\ kg`
`m_p = 50000\ u = 50000 times 1.66 times 10^(-27)\ kg`
Known:
`k = 1.38 times 10^(-23)\ J//K`
Equation:
`v_(rms) = sqrt((2kT)/m)`
solution:
a)
`v_(rms) = sqrt((2kT)/m_a)`
`v_(rms) = sqrt((2(1.38 times 10^(-23)\ J//K)(310\ K))/(89 times 1.66 times 10^(-27)\ kg))`
`v_(rms) = 2.9 times 10^2 m//s`
b)
`v_(rms) = sqrt((2kT)/m_p)`
`v_(rms) = sqrt((2(1.38 times 10^(-23)\ J//K)(310\ K))/(50000 times 1.66 times 10^(-27)\ kg))`
`v_(rms) = 12 m//s` |