Question
The measurement of the electron position is associated with an uncertainty in momentum,
which is equal to $$1 \times {10^{ - 18}}gcm\,\,{s^{ - 1}}.$$ The uncertainty in electron velocity is ( mass of an electron is $$9 \times {10^{ - 28}}g$$ )
A.
$$1 \times {10^9}cm\,\,{s^{ - 1}}$$
B.
$$1 \times {10^6}cm\,\,{s^{ - 1}}$$
C.
$$1 \times {10^5}cm\,\,{s^{ - 1}}$$
D.
$$1 \times {10^{11}}cm\,\,{s^{ - 1}}$$
Answer :
$$1 \times {10^9}cm\,\,{s^{ - 1}}$$
Solution :
$${\text{Given,}}\,\,\Delta p = 1 \times {10^{ - 18}}g\,\,cm\,\,{s^{ - 1}}$$ $${\text{(uncertainty in momentum)}}$$
$$\eqalign{
& {\text{Mass}} = 9 \times {10^{ - 28}}g \cr
& \,\,\,\,\,\Delta p = m\Delta v \cr} $$
$$1 \times {10^{ - 18}} = 9 \times {10^{ - 28}} \times \Delta v$$ $${\text{(uncertainty in velocity)}}$$
$$\Delta v = 1 \times {10^9}cm\,\,{s^{ - 1}}$$