(A) The condition for constructive interference (diffraction) from a crystal lattice is given by Bragg's Law: $2d \sin \theta = n\lambda$.Here,the int

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(A) The condition for constructive interference (diffraction) from a crystal lattice is given by Bragg's Law: $2d \sin \theta = n\lambda$.Here,the interplanar spacing is given as $d = b$.For direct reflection (backscattering),the angle of incidence $\theta$ with respect to the atomic planes is $90^\circ$.Substituting $\theta = 90^\circ$ into Bragg's Law: $2b \sin(90^\circ) = n\lambda$.Since $\sin(90^\circ) = 1$,we get $2b = n\lambda$.Therefore,the wavelength is $\lambda = \frac{2b}{n}$.

Class 12 Physics Dual Nature of Radiation and matter Matter Waves and de Broglie Wavelength

Easy

An electron beam is incident on a crystal. The interplanar spacing of the crystal is $b$. Which of the following de Broglie wavelengths of the electron beam will result in direct reflection?

A
$\lambda = \frac{2b}{n}$
B
$\lambda = \frac{b}{n}$
C
$\lambda = \frac{3b}{n}$
D
$\lambda = \frac{4b}{n}$

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Dual Nature of Radiation and matter

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Matter Waves and de Broglie Wavelength

Find the typical de Broglie wavelength associated with a $He$ atom in helium gas at room temperature $(27^{\circ}C)$ and $1 \; atm$ pressure; and compare it with the mean separation between two atoms under these conditions.

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Two points $A$ and $B$ have potentials of $20 \ V$ and $40 \ V$ respectively. An electron is accelerated from rest between them. Find the de Broglie wavelength associated with the electron at point $B$.

Medium

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An electron,an $\alpha$-particle,and a proton have the same kinetic energy. Which of these particles has the shortest de Broglie wavelength?

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The de Broglie wavelengths of a proton and an $\alpha$ particle are $\lambda$ and $2\lambda$ respectively. The ratio of the velocities of proton and $\alpha$ particle will be:

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If the kinetic energy of a particle is increased to $16$ times, the percentage change in the de Broglie wavelength of a particle is (in $\%$)

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An electron beam is incident on a crystal. The interplanar spacing of the crystal is $b$. Which of the following de Broglie wavelengths of the electron beam will result in direct reflection?

Similar Questions

Find the typical de Broglie wavelength associated with a $He$ atom in helium gas at room temperature $(27^{\circ}C)$ and $1 \; atm$ pressure; and compare it with the mean separation between two atoms under these conditions.

Two points $A$ and $B$ have potentials of $20 \ V$ and $40 \ V$ respectively. An electron is accelerated from rest between them. Find the de Broglie wavelength associated with the electron at point $B$.

An electron,an $\alpha$-particle,and a proton have the same kinetic energy. Which of these particles has the shortest de Broglie wavelength?

The de Broglie wavelengths of a proton and an $\alpha$ particle are $\lambda$ and $2\lambda$ respectively. The ratio of the velocities of proton and $\alpha$ particle will be:

If the kinetic energy of a particle is increased to $16$ times, the percentage change in the de Broglie wavelength of a particle is (in $\%$)

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