12.8 The radius of the innermost electron orbit of a hydrogen atom is 5.3×10–11 m. What are the radii of the n = 2 and n =3 orbits?

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Vishal Baghel | Contributor-Level 10

7 months ago

12.8 The radius of the innermost orbit of a hydrogen atom, $r_{1}$ = 5.3 $* 10^{- 11}$ m

Let $r_{2}$ be the radius of the orbit at n = 2. The relation between the radius of the orbit is

$r_{2}$ = $n^{2} * r_{1}$ =4 $* 5.3 * 10^{- 11} m$ =21.2 $* 10^{- 11} m$

Let $r_{3}$ be the radius of the orbit at n = 3. The relation between the radius of the orbit is

$r_{3}$ = $n^{2} * r_{1}$ =9 $* 5.3 * 10^{- 11} m$ =47.7 $* 10^{- 11} m$

12.8 The radius of the innermost orbit of a hydrogen atom, <math> <msub> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </math> = 5.3 <math> <mo>*</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>11</mn> </mrow> </mrow> </msup> </math> mLet <math> <msub> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </math> be the radius of the orbit at n = 2. The relation between the radius of the orbit is <math> <msub> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msub> </math> = <math> <msup> <mrow> <mrow> <mi>n</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>*</mo> <msub> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </math> =4 <math> <mo>*</mo> <mi> </mi> <mn>5.3</mn> <mo>*</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>11</mn> </mrow> </mrow> </msup> <mi mathvariant="normal"> </mi> <mi mathvariant="normal">m</mi> </math> =21.2 <math> <mo>*</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>11</mn> </mrow> </mrow> </msup> <mi mathvariant="normal"> </mi> <mi mathvariant="normal">m</mi> </math> Let <math> <msub> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </msub> </math> be the radius of the orbit at n = 3. The relation between the radius of the orbit is <math> <msub> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </msub> </math> = <math> <msup> <mrow> <mrow> <mi>n</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>*</mo> <msub> <mrow> <mrow> <mi>r</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </msub> </math> =9 <math> <mo>*</mo> <mi> </mi> <mn>5.3</mn> <mo>*</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>11</mn> </mrow> </mrow> </msup> <mi mathvariant="normal"> </mi> <mi mathvariant="normal">m</mi> </math> =47.7 <math> <mo>*</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>11</mn> </mrow> </mrow> </msup> <mi mathvariant="normal"> </mi> <mi mathvariant="normal">m</mi> </math>

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12.8 The radius of the innermost electron orbit of a hydrogen atom is 5.3×10–11 m. What are the radii of the n = 2 and n =3 orbits?

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