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The lattice parameter for Bragg reflections from plane 110 is = 0.242 nm

The lattice parameter for Bragg reflections from plane 200 is = 0.296 nm

The lattice parameters 0.242 nm and 0.296 nm are not equal,hence metal is not bcc.

The lattice parameter for Bragg reflections from plane 111 is = 0.296 nm

The lattice parameter for Bragg reflections from plane 200 is = 0.296 nm

The lattice parameters 0.296 nm and 0.296 nm are equal,hence metal is fcc.
The atomic diameter is = 0.2093 nm