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BITSAT 2023Paper 2
Exam
BITSAT
Year
2023
Paper
Paper 2
Subject
Chemistry
Chapter
Structure of Atom

BITSAT 2023 · Paper 2 · Chemistry · Structure of Atom

If the radius of the 3 rd Bohr's orbit of hydrogen atom is r_3 and...

If the radius of the 3rdBohr′sorbitofhydrogenatomis3 \mathrm{rd} Bohr's orbit of hydrogen atom isr_3andtheradiusofand the radius of4^{th \text{th }}Bohr′sorbitisBohr's orbit isr_4.Then:. Then:

Options

  1. Ar4=916r3r_4=\frac{9}{16} r_3
  2. Br4=169r3r_4=\frac{16}{9} r_3
  3. Cr4=34r3r_4=\frac{3}{4} r_3
  4. Dr4=43r3r_4=\frac{4}{3} r_3

Correct answer

B. r4=169r3r_4=\frac{16}{9} r_3

Step-by-step solution


r=0.529×n2ZA˚r3=0.529×321⇒r4=0.529×421r4r3=4232=169⇒r4=16r39\begin{aligned} & r=0.529 \times \frac{n^2}{Z} Å \\ & r_3=0.529 \times \frac{3^2}{1} \Rightarrow r_4=0.529 \times \frac{4^2}{1} \\ & \frac{r_4}{r_3}=\frac{4^2}{3^2}=\frac{16}{9} \Rightarrow r_4=\frac{16 r_3}{9}\end{aligned}
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