The speed of a certain proton is 350 km/s. if the uncertainty in its momentum is 0.100%, what is the necessary uncertainty in its location?
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Ответ:
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 ×
g
so momentum will be = m × v
momentum = 1.6726 ×
× 350000
momentum = 5.85 ×
gm/s
momentum = 5.85 ×
gcm/s
and
uncertainty momentum is = 0.1 % × momentum
uncertainty momentum is = 0.1 % × 5.85 ×![10^{-17}](/tpl/images/0222/7670/01511.png)
uncertainty momentum is = 5.85 ×
gcm/s
uncertainty momentum is = 5.85 ×
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 ×
kgm²/s
so put here value in equation 1 and find dx
dx × 5.85 ×
= 1/2× 1.055 × ![10^{-34}](/tpl/images/0222/7670/af661.png)
dx = 9.0 ×
m
dx = 0.90 nm
so necessary uncertainty is 0.90 nm
Ответ:
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