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Q.

Assume that the de-Broglie wave associated with an electron can form a standing wave between the atoms arranged in a one-dimensional array with nodes at each of the atomic sites. It is found that one such standing wave is formed if the distance d between the atoms of the array is  1.2A. A similar standing wave is again formed if d is increased to 1.5A but not for any intermediate value of d. Least value of d in A is equal to

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a

1.2 

b

0.6 

c

0.3 

d

0.1

answer is C.

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Detailed Solution

The standing waves formed by the electron are as shown below.

Question Image

In subsequent loop there will be one more loop as shown in the figures. Clearly, from the diagram sixe of one loop is 0.3 Ao. So in the basic mode of standing wave formation, distance between atoms should atleast be  0.3  Ao

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Assume that the de-Broglie wave associated with an electron can form a standing wave between the atoms arranged in a one-dimensional array with nodes at each of the atomic sites. It is found that one such standing wave is formed if the distance d between the atoms of the array is  1.2A∘. A similar standing wave is again formed if d is increased to 1.5A∘ but not for any intermediate value of d. Least value of d in A∘ is equal to