For an electron whose positional uncertainty is 1.0× 10- 10 m , the uncertainty in the component of the velocity in m s- 1 will be

Question

For an electron whose positional uncertainty is 1.0× 10- 10 m , the uncertainty in the component of the velocity in m s- 1 will be (A) 5.8 × 105 (B) 109 (C) 102 (D) 1015

Tardigrade Admin · Accepted Answer

According to uncertainty principle ⇒ δ x × δ p =( h /4 π ) ⇒ δ p =( h /4 π × δ x ) ⇒ m δ v =( h /4 π δ x ) δ v=(h/4 π m δ x) =(6.625 × 10-34/9.1 × 10-31 × 10-10 × 4 × 3.14)=5.8 × 105

Q. For an electron whose positional uncertainty is $1.0 \times 1 0^{- 10} m$ , the uncertainty in the component of the velocity in m $s^{- 1}$ will be

$5.8 \times 1 0^{5}$

$1 0^{9}$

$1 0^{2}$

$1 0^{15}$

Q. For an electron whose positional uncertainty is 1.0×10−10m , the uncertainty in the component of the velocity in m s−1 will be

5.8×105

109

102

1015

According to uncertainty principle ⇒δx×δp=4πh​ ⇒δp=4π×δxh​ ⇒mδv=4πδxh​ δv=4πmδxh​ =9.1×10−31×10−10×4×3.146.625×10−34​=5.8×105

Q. For an electron whose positional uncertainty is $1.0 \times 1 0^{- 10} m$ , the uncertainty in the component of the velocity in m $s^{- 1}$ will be

$5.8 \times 1 0^{5}$

$1 0^{9}$

$1 0^{2}$

$1 0^{15}$