Question

(a) Assume an electron in the ground state of the hydrogen atom moves at an average...

(a) Assume an electron in the ground state of the hydrogen atom moves at an average speed of 5.00 × 10^6 m/s. If the speed is known to an uncertainty of 1 percent, what is the minimum uncertainty in its position? The radius of the hydrogen atom in the ground state is 5.29 × 10^−11 m. The mass of an electron is 9.1094 × 10^−31 kg.

__________× 10______ m

(b) A 0.13−kg baseball thrown at 100 mph has a momentum of 5.9 kg · m/s. If the uncertainty in measuring the mass is 1.0 × 10^−7 of the mass, calculate the uncertainty in the baseball's position.

__________× 10______ m

Homework Answers

Answer #1


a) uncertainty principle

DX*DV = h/4*pi*m

DX = uncertainty in position = ?

DV = uncertainty in velocity = 5.00*10^6*1/100 = 5.00*10^4 m/s

h = planks constant = 6.625*10^-34 j.s

pi = 3.14

m = mass of electron = 9.1094*10^-31 kg

x*(5.00*10^4) = (6.625*10^-34)/(4*3.14*9.1094*10^-31)

DX = uncertainty in position = x = 1.158*10^-9 m

b)

DX*Dp = h/4*pi

DX = uncertainty in position = ?

Dp = uncertainty in momentum = (5.9/0.13)*1.0*10^-7 = 4.54*10^-6

h = planks constant = 6.625*10^-34 j.s

pi = 3.14

x*4.54*10^-6 = ((6.625*10^-34)/(4*3.14))

DX = uncertainty in position = x = 1.162*10^-29 m

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