Uncertainty in position of an electron (mass of an electron is =9.1 × 10-28 g ) moving with a velocity of 3 × 104 cm / s accurate upto 0.001 % will be (use (h/4 π) in uncertainty expression where h=6.626 × 10-27 erg s)

Question

Uncertainty in position of an electron (mass of an electron is =9.1 × 10-28 g ) moving with a velocity of 3 × 104 cm / s accurate upto 0.001 % will be (use (h/4 π) in uncertainty expression where h=6.626 × 10-27 erg s) (A) 1.93 cm (B) 3.84 cm (C) 5.76 cm (D) 7.68 cm

Tardigrade Admin · Accepted Answer

According to Heisenberg's uncertainty principle

Δ x \times Δ v = \frac{h}{4 πm}

here,

Δ x

= uncertainty in position

Δ v

= uncertainty in velocity

h =

Planck's constant

(6.626 \times 1 0^{- 27} J s)

m =

mass of electron

(9.1 \times 1 0^{- 28} k g)

Here,

Δ v = 0.001%

of

3 \times 1 0^{4}

= \frac{0.001}{100} \times 3 \times 1 0^{4} = 0.3 c m / s

∴ Δ x = \frac{h}{4 πm Δ v}

= \frac{6.626 \times 1 0 ^{- 27}}{4 \times 3.14 \times 9.1 \times 1 0 ^{- 28} \times 0.3} = 1.93 c m

Q. Uncertainty in position of an electron (mass of an electron is =9.1×10−28g ) moving with a velocity of 3×104cm/s accurate upto 0.001% will be (use 4πh​ in uncertainty expression where h=6.626×10−27 erg s)

1.93 cm

3.84 cm

5.76 cm

7.68 cm

Q. Uncertainty in position of an electron (mass of an electron is $= 9.1 \times 1 0^{- 28} g$ ) moving with a velocity of $3 \times 1 0^{4} c m / s$ accurate upto $0.001%$ will be (use $\frac{h}{4 π}$ in uncertainty expression where $h = 6.626 \times 1 0^{- 27}$ erg s)