An element M crystallises in a body centred cubic unit cell with a cell edge of 300 pm. The density of the element is 6.0g cm^-3. The number of atoms in 180g of the element is_________× 10²³ (Nearest integer)

<p><u><span lang="EN-IN">B.C.C structure </span></u></p><p><span lang="EN-IN">a = 300 pm = 300 × 10</span>^{<span lang="EN-IN">-</span>}^{<span lang="EN-IN">12</span>}<span lang="EN-IN"> m</span></p><p><span lang="EN-IN">d = 6g/cm³</span></p><p><span lang="EN-IN">z = 2</span></p><p><span contenteditable="false"> <math> <mrow> <mi>d</mi> <mo>=</mo> <mfrac> <mrow> <mi>Z</mi> <mo>×</mo> <mi>M</mi> </mrow> <mrow> <msup> <mrow> <mi>a</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </math> </span></p><p><span contenteditable="false"> <math> <mrow> <mn>6</mn> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mo>×</mo> <mi>A</mi> </mrow> <mrow> <msup> <mrow> <mrow> <mo> (</mo> <mrow> <mn>3</mn> <mn>0</mn> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>1</mn> <mn>0</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mrow> <mrow> <mn>3</mn> </mrow> </msup> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mo>×</mo> <mi>A</mi> </mrow> <mrow> <mn>2</mn> <mn>7</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mo>−</mo> <mn>2</mn> <mn>4</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </math> </span>&nbsp;</p><p><span lang="EN-IN"><span contenteditable="false"> <math> <mrow> <mo>∴</mo> <mi>A</mi> <mi>t</mi> <mi>o</mi> <mi>m</mi> <mi>s</mi> <mtext> </mtext> <mtext> </mtext> <mi>o</mi> <mi>f</mi> <mtext> </mtext> <mtext> </mtext> <mi>M</mi> </mrow> </math> </span> = 3.69 × 6.022 × 10²³</span></p><p><span lang="EN-IN">= 22.22 × 10²³</span></p><p><span lang="EN-IN">the nearest integer = 22</span></p><p><span lang="EN-IN">&nbsp;</span></p>

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