Calculate the mass of an elementary particle, | vedclass

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

Question

(D) Given: Precision $= \pm 1 \%$,$\Delta x = 1.05 	imes 10^{-13} \ m$,$h = 6.6 	imes 10^{-34} \ kg \ m^2 \ s^{-1}$.Velocity of light $c = 3 	imes

Vedclass · Accepted Answer

$0.8 	imes 10^{-28} \ kg$

Vedclass · Answer

(D) Given: Precision $= \pm 1 \%$,$\Delta x = 1.05 	imes 10^{-13} \ m$,$h = 6.6 	imes 10^{-34} \ kg \ m^2 \ s^{-1}$.Velocity of light $c = 3 	imes 10^8 \ m/s$.Particle velocity $v = 2c = 6 	imes 10^8 \ m/s$.Uncertainty in velocity $\Delta v = 1 \% 	ext{ of } v = 0.01 	imes 6 	imes 10^8 = 6 	imes 10^6 \ m/s$.According to Heisenberg's Uncertainty Principle: $\Delta x \cdot m \cdot \Delta v \ge \frac{h}{4 \pi}$.$m = \frac{h}{4 \pi \cdot \Delta x \cdot \Delta v}$.$m = \frac{6.6 	imes 10^{-34}}{4 	imes 3.14 	imes 1.05 	imes 10^{-13} 	imes 6 	imes 10^6}$.$m = \frac{6.6 	imes 10^{-34}}{79.128 	imes 10^{-7}} \approx 0.0834 	imes 10^{-27} \ kg = 0.834 	imes 10^{-28} \ kg$.Rounding to the nearest provided option,the correct value is $0.8 	imes 10^{-28} \ kg$.

Calculate the mass of an elementary particle,which is accelerated to twice the velocity of light with the precision $\pm 1 \%$,and has $1.05 \times 10^{-13} \ m$ uncertainty in position. $(h = 6.6 \times 10^{-34} \ kg \ m^2 \ s^{-1})$

Similar Questions

$A$ particle of mass $25 \, g$ has an uncertainty in position of $10^{-5} \, m$. The uncertainty in velocity is ... (Planck's constant $h = 6.6 \times 10^{-34} \, J \cdot s$).

If uncertainty in the measurement of position and momentum of a microscopic object of mass $m$ are equal,then the uncertainty in the measurement of velocity is given by the expression:

The uncertainty principle and the concept of wave nature of matter were proposed by ...... and ...... respectively.

The Heisenberg uncertainty principle is not valid for

If the uncertainty in the position of an electron is associated with an uncertainty in momentum of $2 \times 10^{-17} \ g \ cm \ s^{-1}$,what will be the uncertainty in the velocity of the electron?

Vedclass Test Series

Exam Paper Generator

Online Exam Module