According to Bohr's model of hydrogen atom, which of the following statement is incorrect?

According to Bohr's model of hydrogen atom, which of the following statement is incorrect?
  1. Radius of \(3^{\text {rd }}\) orbit is nine times larger than that of \(1^{\text {st }}\) orbit.
  2. Radius of \(8^{\text {th }}\) orbit is four times larger than that of \(4^{\text {th }}\) orbit.
  3. Radius of \(6^{\text {th }}\) orbit is three time larger than that of \(4^{\text {th }}\) orbit.
  4. Radius of \(4^{\text {th }}\) orbit is four times larger than that of \(2^{\text {nd }}\) orbit.

Solution

\(\mathrm{r} \propto \mathrm{n}^2\)
(1) \(\frac{\mathrm{r}_3}{\mathrm{r}_1}=\frac{9}{1}\)
(2) \(\frac{\mathrm{r}_8}{\mathrm{r}_4}=\frac{64}{16}=4\)
(3) \(\frac{\mathrm{r}_6}{\mathrm{r}_4}=\left(\frac{6}{4}\right)^2=\frac{9}{4}\)
(4) \(\frac{\mathrm{r}_4}{\mathrm{r}_2}=\left(\frac{4}{2}\right)^2=4\)

Asked in: JEE Main 2025 (02 Apr Shift 1)

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