Question

Uncertainty in position of an electron (mass = 9.1 x
10^-28 gm) moving with a velocity of 3 x 10^4 cm/s
accurate upto 0.001% will be (Use h/4π) in uncertainty
expression where h = 6.626 x 10^-27 erg-s)
(1) 5.76 cm
(2) 7.68 cm
(3) 1.93 cm
(4) 3.84 cm​

Answer 1

Answer:

Option (3) 1.93 cm

Explanation:

Mass of the electron = 9.1 × 10^-28 gm = 9.1 × 10^-31 kg

Velocity of the electron = 3 × 10^4 cm/s = 3 × 10^2 m/s

Momentum of the electron

p = mv

or, $p=9.1\times 10^{-31}\times 3\times 10^{2}$ kg-m/s

$\implies p=27.3\times 10^{-29}$ kg-m/s

0.001% of p

= $\frac{0.001}{100}\times 27.3\times 10^{-29}$

= $27.3\times 10^{-34}$ kg-m/s

Using the uncertainity principle

$x.p=\frac{h}{4\pi}$

$\implies x=\frac{h}{4p\pi}$

$\implies x=\frac{6.626\times 10^{-34}}{4\times3.14\times 27.3\times10^{-34}}$        (∵ h = 6.626 × 10^-34 Js)

$\implies x=0.0193$ m

or, x = 1.93 cm

Hope this helps

Answer 2

Answer:

Explanation:

Mass of the electron = 9.1 × 10^-28 gm = 9.1 × 10^-31 kg

Velocity of the electron = 3 × 10^4 cm/s = 3 × 10^2 m/s

Momentum of the electron

p = mv

or,  kg-m/s

kg-m/s

0.001% of p

=

=  kg-m/s

Using the uncertainity principle

       (∵ h = 6.626 × 10^-34 Js)

m

or, x = 1.93 cm

Hope this helps

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