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De Broglie's Hypothesis

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Question

Similar to electron diffraction, neutron diffraction microscope is also used for the determination of the structure of molecules. If the wavelength used here is 800 pm, calculate the characteristic velocity associated with the neutron.

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Solution

From de Broglie’s equation,
$λ = \frac{h}{m v} v = \frac{h}{m λ}$
Where, v = velocity of particle
(neutron) h = Planck’s constant
m = mass of particle (neutron)
λ = wavelength
Substituting the values in the expression of velocity (v),
$v = \frac{6.626 \times 10^{- 34} J s}{(1.67493 \times 10^{- 27} k g) (800 \times 10^{- 12} m)} = 4.94 \times 10^{2} m s^{- 1} = 494 m s^{- 1}$
$∴$ Velocity associated with the neutron = 494 m $s^{- 1}$

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Similar questions

Q. Neutron diffraction pattern is used to determine :

Q. (a) Obtain the de Broglie wavelength of a neutron of kinetic energy 150 eV. As you have seen in Exercise 11.31, an electron beam of this energy is suitable for crystal diffraction experiments. Would a neutron beam of the same energy be equally suitable? Explain. (mn = 1.675 × 10–27 kg) (b) Obtain the de Broglie wavelength associated with thermal neutrons at room temperature (27 °C). Hence explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments.

Q. (a) Obtain the de Broglie wavelength of a neutron of kinetic energy 150 eV. As you have seen in Exercise 11.31, an electron beam of this energy is suitable for crystal diffraction experiments. Would a neutron beam of the same energy be equally suitable? Explain.(

m_{n} = 1.675 \times 10^{27}

kg)
(b) Obtain the de Broglie wavelength associated with thermal neutrons at room temperature (

27^{o} C

). Hence, explain why a fast neutron beam needs to be thermalised with the environment before it can be used for neutron diffraction experiments.

Exercise 11.31:

Crystal diffraction experiments can be performed using X-rays, or electrons accelerated through appropriate voltage. Which probe has greater energy? (For quantitative comparison, take the wave length of the probe equal to 1

A∘A∘ which is of the order of inter-atomic spacing in the lattice) (

m_{e} = 9.11 \times 10^{- 31} k g

Q. Dual behaviour of matter proposed by de Broglie led to the discovery of electron microscope often used for the highly magnified images of biological molecules and other type of material. If the velocity of the electron in this microscope is

1.6 \times 10^{6} {m s}^{- 1}

, calculate de Broglie wavelength associated with this electron.

Q. Dual behaviour of the matter proposed by de Broglie led to the discovery of electron microscope often used for the highly magnified images of biological molecules and other types of material. If the velocity of the electrons in this microscope is

1.6 \times 10^{6}

m s^{- 1}

, calculate de Broglie wavelength associated with this electron.

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De Broglie's Hypothesis

Standard XII Chemistry

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