Dual Nature of Matter and Radiation Test

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Dual Nature of Matter and Radiation Test - 3

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Question 1
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Directions For Questions

Directions: The following question has four choices out of which ONLY ONE is correct.

De Broglie used Einstein's special theory of relatively together with Plank's quantum theory to establish the wave property of particles. He gave fundamental relationship λ h/p ; where λ and p is wavelength and momentum respectively and h is Plank's constant. A de-Broglile wave associated with an electron can form a standing wave between the atoms arranged in a one dimensional array with node at each of the atomic sites. A standing wave is formed when the distance between the atoms of any array is d = 3A^o_^. A similar standing wave is again formed if d = 3.5 A^o but not for any intermediate value of d.

For thermal neutron at ordinary temperature, energy is given by relation E = kT, where K is Boltzman constant mass of Neutron is 1.67 ×10^–23 g.

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The least value of d for which standing wave can be formed is

A
3 A^o

B
0.5 A^o

C
1 A^o

D
1.5 A^o

Solution

The min distance for which the standing wave would be formed would be equal to the min difference between the atomic spacings, which is 0.5 A^o.