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 Rn=0.529 Ao *n2z Radius of Bohr's orbit for hydrogen, Rn=0.529 Ao *n2 For third orbit (R3) = 0.529 Ao *9 = r3 and Fourth orbit (R4) = 0.59 Ao *16=r4 ∴r4=16r39

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 - <math> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>9</mn> </mrow> <mrow> <mn>1</mn> <mn>6</mn> </mrow> </mfrac> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </math>

Option 2 - <math> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mn>6</mn> </mrow> <mrow> <mn>9</mn> </mrow> </mfrac> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </math>

Option 3 - <math> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </math>

Option 4 - <math> <mrow> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>4</mn> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> <msub> <mrow> <mi>r</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </math>

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Payal Gupta | Contributor-Level 10

8 months ago

Correct Option - 2

Detailed Solution:

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

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

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

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

$∴ r_{4} = \frac{16 r_{3}}{9}$

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