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The uncertainty in the position of an el...

The uncertainty in the position of an electron `(mass = 9.1 xx 10^-28 g)` moving with a velocity of `3.0 xx 10^4 cm s^-1` accurate up to `0.001 %` will be
(Use `(h)/(4 pi)` in the uncertainty expression, where `h = 6.626 xx 10^-27 erg - s`)

A

`1.93` cm

B

`3.84` cm

C

`5.76` cm

D

`7.68` cm

Text Solution

Verified by Experts

The correct Answer is:
A
Given mass of an electron (m) ` = 9.1 xx 10^(-28) g`
Velocity of electron (v) ` =3 xx10^(4) cm//s`:
Accuray in velocity =` 0.001% = (0.001)/(100)`
Actual velocity of the electron
`(Delta V) = 3 xx 10^(4) xx (0.001)/(100) = 0.3 cm//s`
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Knowledge Check

  • The uncertainty in the position of an electron (mass =9.1xx10^(-28) g) moving with a velocity of 3.0xx10^(4) cm s^(-1) accurate upto 0.011 % will be

    A
    1.92 cm
    B
    7.68 cm
    C
    0.175 cm
    D
    3.84 cm

  • The uncertainty in the position of an electron (mass =9.1xx10^(-28)g ) moving with a velocity of 3.0xx10^(4) cms^(-1) accurate up to 0.011% will be

    A
    1.92 cm
    B
    7.68 cm
    C
    0.175 cm
    D
    3.84 cm

  • Uncertainty in the position of an electron mass (9. 1 xx 10^(31) kg) moving with a velocity 300 ms^(-1) accurate uptp 0.001 % will be :

    A
    ` 19 . 2 xx 10^(-2) m`
    B
    ` 5. 75 xx 10^(-2) m`
    C
    `1. 92 xx 10^(-5) m`
    D
    `3. 584 xx 10^(-2) m`

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