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GUJCET · Physics · Atoms
Ratio of radii of second and third orbits of H －atom is _________.
- A \(3: 2\)
- B \(2: 3\)
- C \(9: 4\)
- D \(4: 9\)
Answer & Solution
Correct Answer
(D) \(4: 9\)
Step-by-step Solution
Detailed explanation
(D) \(4: 9\)
Radius \(r_{n} \propto \frac{n^{2}}{\mathrm{Z}}\)
But for H -atom \(\mathrm{Z}=1\)
\(\therefore \quad r_{n} \propto n^{2}\)
\(\therefore \quad \frac{r_{2}}{r_{3}}=\left(\frac{n_{2}}{n_{3}}\right)^{2}\)
\(\therefore \quad \frac{r_{2}}{r_{3}}=\left(\frac{2}{3}\right)^{2}\)
\(\therefore \quad \frac{r_{2}}{r_{3}}=\frac{4}{9}\)
Radius \(r_{n} \propto \frac{n^{2}}{\mathrm{Z}}\)
But for H -atom \(\mathrm{Z}=1\)
\(\therefore \quad r_{n} \propto n^{2}\)
\(\therefore \quad \frac{r_{2}}{r_{3}}=\left(\frac{n_{2}}{n_{3}}\right)^{2}\)
\(\therefore \quad \frac{r_{2}}{r_{3}}=\left(\frac{2}{3}\right)^{2}\)
\(\therefore \quad \frac{r_{2}}{r_{3}}=\frac{4}{9}\)
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