If a proton is accelerated to a velocity of 3 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The uncertainty in velocity $\Delta v$ is given by $0.5 \%$ of $3 	imes 10^7 	ext{ ms}^{-1}$.$\Delta v = \frac{0.5}{100} 	imes 3 	imes 10^7

Vedclass · Accepted Answer

$2.11 	imes 10^{-13} 	ext{ m}$

Vedclass · Answer

(D) The uncertainty in velocity $\Delta v$ is given by $0.5 \%$ of $3 	imes 10^7 	ext{ ms}^{-1}$.$\Delta v = \frac{0.5}{100} 	imes 3 	imes 10^7 	ext{ ms}^{-1} = 1.5 	imes 10^5 	ext{ ms}^{-1}$.According to Heisenberg's uncertainty principle,$\Delta x 	imes \Delta p \ge \frac{h}{4 \pi}$.Since $\Delta p = m \Delta v$,we have $\Delta x = \frac{h}{4 \pi m \Delta v}$.Substituting the values: $\Delta x = \frac{6.6 	imes 10^{-34}}{4 	imes 3.14 	imes 1.66 	imes 10^{-27} 	imes 1.5 	imes 10^5}$.$\Delta x = \frac{6.6 	imes 10^{-34}}{31.27 	imes 10^{-22}} \approx 2.11 	imes 10^{-13} 	ext{ m}$.

If a proton is accelerated to a velocity of $3 \times 10^7 \text{ ms}^{-1}$ which is accurate up to $\pm 0.5 \%$,then the uncertainty in its position will be $\ldots \ldots \ldots$ [mass of proton $= 1.66 \times 10^{-27} \text{ kg}$,$h = 6.6 \times 10^{-34} \text{ Js}$]

Similar Questions

Choose the correct statement.

The simultaneous determination of the exact position and momentum of an electron is:

$A$ microscope using suitable photons is employed to locate an electron in an atom within a distance of $0.1 \, \mathring{A}$. What is the uncertainty involved in the measurement of its velocity?

The wave mechanical model of atom is based upon

If the position of the electron was measured with an accuracy of $\pm 0.002 \ nm$,the uncertainty in the momentum of it would be (in $kg \ ms^{-1}$) $(h=6.626 \times 10^{-34} \ J \ s)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module