NCERT Class XI Chemistry Structure of Atom Solutions

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Question : 61
Total: 67
If the position of the electron is measured within an accuracy of ± 0.002 nm, calculate the uncertainty in the momentum of the electron. Suppose the momentum of the electron is
h
4πm×0.05nm
, is there any problem in defining this value.
Solution:  
According to uncertainty principle, Δx Δp =
h
4π

where, Δx = ± 0.002 nm = ± 0.002 × 109m, Δp = ? ∴ Δp =
h
4πΔx
=
6.626×1034
4×
22
7
×0.002
×109
= 2.63 × 1023kgmsec
Actual momentum =
h
4πm
.
1
0.05
=
6.626×1034
4×3.14×5×1011
= 1.05 × 1024kgms
This value cannot be defined as the actual magnitude of the momentum is smaller than the uncertainty in momentum, which is impossible.
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