Question

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)

JEE/Engineering Exams

Chemistry

Solution

116

4.0 (1 ratings)

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} ]