Question

what is the uncertainty of the position of the bacterium ?

<Chapter 2 The Heisenberg Uncertainty Principle Part A A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of m = 1.50 fg (where a femtogram, fg, is 10-15 g) and is swimming at a velocity of u = 7.00 pm/s, with an uncertainty in the velocity of 6.00%. E. coli bacterial cells are around 1 um (10 m) in length. The student is supposed to observe the bacterium and make a drawing. However, the student, having just learned about the Heisenberg uncertainty principle in physics class, complains that she cannot make the drawing. She claims that the uncertainty of the bacterium's position is greater than the microscope's viewing field, and the bacterium is thus impossible to locate. What is the uncertainty of the position of the bacterium? Express your answer with the appropriate units. ► View Available Hint(s) Az = 5.50 . 10-10 Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining Part B Complete previous part(s) Provide Feedback

Answer 1

Mass of bacteria [m] = 1.5 fg = 1.5 ×10⁻¹⁵ g

uncertainty in velocity = 6.00 % = 6 / 100 = 0.06

Velocity of bacteria [v] = 7.00 um/s = 7 x 10^-6 m/s

uncertainty in velocity = Δv = 0.06 x [7 x 10^-6] m/s = 4.2 x 10^-7 m/s

uncertainty in momentum = Δp = mΔv = (1.5 ×10⁻¹⁵ g) x (4.2 x 10^-7 m/s)

uncertainty in position Δx = (h/4π ) / mΔv = [ 6.62606957 ×10⁻³¹ m²gs⁻¹ / 4 x 3.14] / [(1.5 ×10⁻¹⁵ g) x (4.2 x 10^-7 m/s)]

uncertainty in position Δx = 8.3738621e-11 m

Δx = 8.4 x 10^-11 m

<Chapter 2 The Heisenberg Uncertainty Principle Part A A student is examining a bacterium under the microscope. The E. coli bacterial cell has a mass of m = 1.50 fg (where a femtogram, fg, is 10-15 g) and is swimming at a velocity of u = 7.00 pm/s, with an uncertainty in the velocity of 6.00%. E. coli bacterial cells are around 1 um (10 m) in length. The student is supposed to observe the bacterium and make a drawing. However, the student, having just learned about the Heisenberg uncertainty principle in physics class, complains that she cannot make the drawing. She claims that the uncertainty of the bacterium's position is greater than the microscope's viewing field, and the bacterium is thus impossible to locate. What is the uncertainty of the position of the bacterium? Express your answer with the appropriate units. ► View Available Hint(s) CHA + 0 21 ? Ar= 8.4 x 10-11 m Submit Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining Part B Complete previous part(s) Provide Feedback

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