## Related questions with answers

A hydrogen atom is in its first excited state (n = 2). Using the Bohr theory of the atom, calculate the radius of the orbit.

Solutions

VerifiedIn this problem, a hydrogen atom is excited to the first excited state, corresponding to $n = 2$. We use the Bohr model in this problem. For this part, we calculate the radius of the orbit.

Given values:

$n=2$

In part $\textbf{a)}$ we have to find the radius of the orbit.

Using Bohr atomic theory, radius of the hydrogen atom can be calculated as:

$\begin{align*} r_{n}=n^{2}\left[a_{0}\right] \end{align*}$

Hence, for the hydrogen atom we get:

$\begin{align*} r_{n=2}=2^{2}\left[0.0529\textrm{nm}\right] \end{align*}$

Solution is:

$\begin{align*} \boxed{r_{n=2}=0.212\textrm{nm}} \end{align*}$

We have:

$r_n = n^2 \ a_0$

For n=2:

$r_2 = (2)^2 \ a_0 = (4) \ (0.0529 \ nm) = 0.212 \ nm$

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