The wave property of electrons implies that t | vedclass

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

Question

(B) The condition for constructive interference in crystal diffraction (Bragg's Law) is given by $2d \sin 	heta = n \lambda$, where $	heta$ is the g

Vedclass · Accepted Answer

$50$

Vedclass · Answer

(B) The condition for constructive interference in crystal diffraction (Bragg's Law) is given by $2d \sin 	heta = n \lambda$, where $	heta$ is the glancing angle.From the figure, the angle of incidence $i$ is measured with respect to the normal. The glancing angle $	heta$ is the angle between the incident ray and the crystal plane, so $	heta = 90^{\circ} - i$.Given $i = 30^{\circ}$, we have $	heta = 90^{\circ} - 30^{\circ} = 60^{\circ}$.For first-order diffraction, $n = 1$. Substituting the values:$2 	imes (1 	imes 10^{-10}\; m) 	imes \sin(60^{\circ}) = 1 	imes \lambda$$\lambda = 2 	imes 10^{-10} 	imes \frac{\sqrt{3}}{2} = \sqrt{3} 	imes 10^{-10}\; m \approx 1.732 	imes 10^{-10}\; m$.The de-Broglie wavelength of an electron accelerated by potential $V$ is given by $\lambda = \frac{h}{\sqrt{2meV}}$.Squaring both sides:$\lambda^2 = \frac{h^2}{2meV} \Rightarrow V = \frac{h^2}{2me\lambda^2}$.Substituting the values:$V = \frac{(6.6 	imes 10^{-34})^2}{2 	imes 9.1 	imes 10^{-31} 	imes 1.6 	imes 10^{-19} 	imes (\sqrt{3} 	imes 10^{-10})^2}$$V = \frac{43.56 	imes 10^{-68}}{29.12 	imes 10^{-50} 	imes 3} = \frac{43.56 	imes 10^{-68}}{87.36 	imes 10^{-50}} \approx 0.4986 	imes 10^{18} 	imes 10^{-68} 	imes 10^{50} \approx 49.86\; V$.Thus, $V$ should be about $50\; V$.

Similar Questions

Statement $1$: The Davisson-Germer experiment established the wave nature of electrons. Statement $2$: If electrons possess wave nature,they can undergo interference and diffraction.

Which phenomenon best supports the theory that matter has a wave nature?

Which of the following statements is incorrect regarding the Davisson-Germer experiment?

Consider two separate ideal gases of electrons and protons having the same number of particles. The temperature of both gases is the same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to :-

Vedclass Test Series

Exam Paper Generator

Online Exam Module