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Chapter 4: Q23E (page 135)

Question: Atoms in a crystal form atomic planes at many different angles with respect to the surface. The accompanying figure shows the behaviors of representative incident and scattered waves in the Davisson-Germer experiment. A beam of electrons accelerated through 54 V is directed normally at a nickel surface, and strong reflection is detected only at an angle 蠒of 500.Using the Bragg law, show that this implies a spacing D of nickel atoms on the surface in agreement with the known value of 0.22 nm.

Short Answer

Expert verified

Answer:

It is shown that D = 0.22nm .

Step by step solution

01

de Broglie’s formula

The de Broglie鈥檚 wavelength formula is 位=hmv.

02

Proof

Using the formula , V=h22mq位2find the value of as follows:

54V=6.63脳10-34J路s229.11脳10-31kg1.6脳10-19C位2位2=6.63脳10-34J路s2108V9.11脳10-31kg1.6脳10-19C位=6.63脳10-34J路s108V9.11脳10-31kg1.6脳10-19C位=1.67脳10-10鈥�m

From the figure, it is clear that the angle between the incident beam and atomic plate can be obtained as follows:

胃=90掳-蠒2=90掳-50掳2=90掳-25掳=65掳

Using Bragg鈥檚 law, we have:

2dsin胃=m位d=m位2sin胃d=1脳1.67脳10-10m2脳sin65掳d=0.092鈥�nm

The angle between the planes and the crystal surface can be obtained as follows:

胃=90掳-65掳=25掳

Now, by the sine law, we get:

sin胃=dDD=dsin胃D=0.092nmsin25掳D=0.22鈥�nm

Thus, it is proved that spacing has the value D of 0.22nm.

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