Answer:
necessary uncertainty is 0.90 nm
Explanation:
given data
speed v = 350 km/s = 350000 m/s
momentum = 0.1 %
to find out
necessary uncertainty
solution
we know here mass of proton m is 1.6726 × [tex]10^{-24}[/tex] g
so momentum will be = m × v
momentum = 1.6726 × [tex]10^{-24}[/tex] × 350000
momentum = 5.85 × [tex]10^{-19}[/tex] gm/s
momentum = 5.85 × [tex]10^{-17}[/tex] gcm/s
and
uncertainty momentum is = 0.1 % × momentum
uncertainty momentum is = 0.1 % × 5.85 × [tex]10^{-17}[/tex]
uncertainty momentum is = 5.85 × [tex]10^{-20}[/tex] gcm/s
uncertainty momentum is = 5.85 × [tex]10^{-26}[/tex] kgm/s
and we consider here dx is uncertainty position
and dp is uncertainty momentum
so dp × dx = 1/2× h ..................1
h is plank constant that is = 1.055 × [tex]10^{-34}[/tex] kgm²/s
so put here value in equation 1 and find dx
dx × 5.85 × [tex]10^{-26}[/tex] = 1/2× 1.055 × [tex]10^{-34}[/tex]
dx = 9.0 × [tex]10^{-10}[/tex] m
dx = 0.90 nm
so necessary uncertainty is 0.90 nm
