Question 417: Atoms & Nuclei

Question

In hydrogen atom in its ground state, the first Bohr orbit has radius ' $\mathrm{r}_1$ '. When the atom is raised to one of its excited states, the electrons orbital velocity becomes one-third. The radius of that orbit is

Accepted Answer

From Bohr's theory:
Velocity \& radius in nth orbit:
$$ V_n=\frac{V_1}{n} \& r_n=r_1 n^2 $$
From given,
$$ \begin{aligned} & V_n=\frac{V_1}{3} \Rightarrow \frac{V_1}{n}=\frac{V_1}{3} \ 	herefore & n=3 \end{aligned} $$
So, the electron is in the third Bohr orbit.
$$ \begin{array}{ll}  & r_n=r_1 n^2=r_1(3)^2 \ 	herefore \quad & r_n=9 r_1 \end{array} $$

Answer

$2 r_1$

Answer

$3 r_1$

Answer

$4 r_1$

Answer

$9 r_1$

Atoms & Nuclei

In hydrogen atom in its ground state, the first Bohr orbit has radius ' \mathrm{r}_1 '. When the atom is raised to one of its excited states, the electrons orbital velocity becomes one-third. The radius of that orbit is

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