please answer part \"(b)\" with steps! 3 Use the Heisenberg uncertainty principl

Question

please answer part "(b)" with steps!

3 Use the Heisenberg uncertainty principle to answer the following questions (a) A bullet is traveling at 695 m/s in the positive x direction. If the bullet weighs 41 g and the uncertainty in the momentum is 0.17%, how accurately can the position in the x direction be measured? (b) Estimate the diameter of a hydrogen atom (or look it up). If an electron is confined in a 1-D box with a length equal to this diameter, what is the minimum uncertainty in the momentum?

Explanation / Answer

3. a. given v = 695 m/s

m = 41 g

dp = 0.17%

dx = ?

now, from undertianity principle

dx*dp= h/4*pi

now, dp/p= 0.17/100

p = mv

hence

dp = 0.17mv/100 = 0.0484415

hence

dx = g/4*pi*0.0484415 = 10.957169*10^-34 m

b. let diameter of hydrogen atom be l

l = 120*10^-12 m

then

for an electron well this width

lambda = 2l = 240*10^-12 m

hence

from Debroglies wave equaiton

h/mv = lambda

m = 9.1*10^-31 kg

hence

v = 3054029.30402 m/s

now, dl = 120*10^-12 m

hence

dp*dl = h/4*pi

dp = 4.4231*10^-25 kg m/s

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