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Bohr's Model of Atom

Suppose an el...

Question

Suppose an electron beam is used to probe the internal structure of a neutron. The required kinetic energy of the electron is (assume the diameter of a neutron to be of the order of $10^{- 15} m$ ) of the order of

A

1 MeV

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B

10 MeV

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C

100 MeV

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D

1000 MeV

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Solution

The correct option is D
1000 MeV

$λ = \frac{h}{p}, K E = p c = \frac{h}{λ} C s u b s i t i t u t i n g, λ = 10^{3} M e V$

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The wavelength of a probe is roughly a measure of the size of a structure that it can probe in some detail. The quark structure of protons and neutrons appears at the minute length-scale of 10⁻¹⁵ m or less. This structure was first probed in early 1970’s using high energy electron beams produced by a linear accelerator at Stanford, USA. Guess what might have been the order of energy of these electron beams. (Rest mass energy of electron = 0.511 MeV.)

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. (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. An electron, an alpha particle, a proton and a neutron have same de-Broglie wavelength. What would be the order of their kinetic energies ?

Q. In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of

7.5 \times 10^{- 12} m

, the minimum electron energy required is close to

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