Question

According to Heisenberg's uncertainty principle, the product of uncertainties in position ( ( Delta x) ) and velocity ( (Delta v) geq frac{h}{n pi} )
Question says, "accurate up to ( 0.001 %^{prime prime} ). This indicates that the uncertainty in velocity is ( 0.001 % ) of actual value, ( 300 mathrm{m} mathrm{s}^{-1} )
i.e. uncertainty in velocity ( (Delta v)=frac{300 times 0.001}{100} )
[
=3 times 10^{-3} mathrm{m} mathrm{s}^{-1}
]
Therefore, the uncertainty in position ( (Delta x) ) can be calculated as follows:
[
begin{aligned}
Delta x &=frac{h}{4 pi m Delta u}
&=frac{6.626 times 10^{-34} times 100}{4.14 times 9.1 times 10^{-31} times 0.001 times 300}
&=1.93 times 10^{-2} mathrm{m}
end{aligned}
]

# eorumg to Bohr's theory angular momentum of electron in 5th shell is :- (AIEEE-2006 (1) 1.0 h/t (2) 10 h/ (3) 2.5 h/ (4) 25 h/ Uncertainty in the position of an electron (mass = 9.1 x 10-31 Kg) moving with a velocit, 300 ms-, accurate upto 0.001%, will be :- (h = 6.63 x 10-34 Js) (1) 5.76 x10-2 m (2) 1.92 x 10-2 m (3) 3.84 x 10-2 m (4) 19.2 x 10-2 m [AIEEE-2006)

Solution