If the radius of the 3rd Bohr’s orbit of hydrogen atom r3 and the radius of 4th Bohr’s orbit is r4. Then:

Radius of Bohr’s orbit R n = 0 . 5 2 9 A o × n 2 z Radius of Bohr’s orbit for hydrogen, R n = 0 . 5 2 9 A o × n 2 <!- [endif]-><!- [if gte mso 9]><xml> </xml><! [endif]->For third orbit (R3) = 0 . 5 2 9 A o × 9 = r3 andFourth orbit (R4) = 0 . 5 9 A o × 1 6 = r 4 <!- [endif]-><!- [if gte mso 9]><xml> </xml><! [endif]-> ∴ r 4 = 1 6 r 3 9

If the radius of the 3rd Bohr’s orbit of hydrogen atom r3 and the radius of 4th Bohr’s orbit is r4. Then:

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Bohr's Model of Hydrogen Atom Structure of Atom Chemistry Class 11th

If the radius of the 3^rd Bohr’s orbit of hydrogen atom r₃ and the radius of 4^th Bohr’s orbit is r₄. Then:

Option 1 -

$r_{4} = \frac{9}{16} r_{3}$

Option 2 -

$r_{4} = \frac{16}{9} r_{3}$

Option 3 -

$r_{4} = \frac{3}{4} r_{3}$

Option 4 -

$r_{4} = \frac{4}{3} r_{3}$

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Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 2

Detailed Solution:

Radius of Bohr’s orbit $R_{n} = 0.529 \overset{o}{A} \times \frac{n^{2}}{z}$

Radius of Bohr’s orbit for hydrogen, $R_{n} = 0.529 \overset{o}{A} \times n^{2}$

For third orbit (R₃) = $0.529 \overset{o}{A} \times 9$ = r₃ and

Fourth orbit (R₄) = $0.59 \overset{o}{A} \times 16 = r_{4}$

$∴ r_{4} = \frac{16 r_{3}}{9}$

Radius of Bohr’s orbit <math> <mrow> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>5</mn> <mn>2</mn> <mn>9</mn> <mtext> </mtext> <mtext> </mtext> <mover> <mrow> <mi>A</mi> </mrow> <mrow> <mi>o</mi> </mrow> </mover> <mtext> </mtext> <mtext> </mtext> <mo>×</mo> <mfrac> <mrow> <msup> <mrow> <mi>n</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>z</mi> </mrow> </mfrac> </mrow> </math>  Radius of Bohr’s orbit for hydrogen,   <math> <mrow> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mn>5</mn> <mn>2</mn> <mn>9</mn> <mtext> </mtext> <mtext> </mtext> <mover> <mrow> <mi>A</mi> </mrow> <mrow> <mi>o</mi> </mrow> </mover> <mtext> </mtext> <mtext> </mtext> <mo>×</mo> <msup> <mrow> <mi>n</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </mrow> </math> <!- [endif]-><!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1819530504"> </o:OLEObject></xml><! [endif]->For third orbit (R3) = <math> <mrow> <mn>0</mn> <mo>.</mo> <mn>5</mn> <mn>2</mn> <mn>9</mn> <mtext> </mtext> <mtext> </mtext> <mover> <mrow> <mi>A</mi> </mrow> <mrow> <mi>o</mi> </mrow> </mover> <mtext> </mtext> <mtext> </mtext> <mo>×</mo> <mn>9</mn> </mrow> </math> = r3 andFourth orbit (R4) = <math> <mrow> <mn>0</mn> <mo>.</mo> <mn>5</mn> <mn>9</mn> <mtext> </mtext> <mtext> </mtext> <mover> <mrow> <mi>A</mi> </mrow> <mrow> <mi>o</mi> </mrow> </mover> <mtext> </mtext> <mtext> </mtext> <mo>×</mo> <mn>1</mn> <mn>6</mn> <mo>=</mo> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msub> </mrow> </math> <!- [endif]-><!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1819530506"> </o:OLEObject></xml><! [endif]-> <math> <mrow> <mo>∴</mo> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mn>6</mn> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> <mrow> <mn>9</mn> </mrow> </mfrac> </mrow> </math>

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If the radius of the 3^rd Bohr’s orbit of hydrogen atom r₃ and the radius of 4^th Bohr’s orbit is r₄. Then:

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