Determine the expected diffraction angle for the first-order reflection from the (113) set of planes for FCC platinum when monochromatic radiation of wavelength 0.1542 nm is used. The radius for platinum is 0.1387 nm.

2Θ = 81.34⁰

Explanation:

We have the plane = 113

The material = fcc platinum

Lambda L, = 0.1542

n = 1

Lambda = 2dsinΘ (1)

d = a/√h²+k²+l² (2)

We have been given the atomic radius to be

R = 0.1387nm

For FCC we have

a = 2R√2

= 2x0.1387x√2

= 0.3923nm

From the second equation

d111 = 0.3923nm/√1²+1²+3²

= 0.3923/√11

= 0.1183nm

From the first equation

0.1542 = 2x0.1183nmSinΘ

0.1542 = 0.2366sinΘ

SinΘ = 0.1542/0.2366

= 0.6517

Θ = Sin-1(0.6517)

= 40.67

2Θ = 81.34⁰

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