Question 31: Atoms & Nuclei

Question

According to Bohr's theory of hydrogen atom, the speed of the electron, its energy and radius of its orbit vary with the principal quantum number $n$, respectively as

Accepted Answer

In the Bohr model for hydrogen (or any oneÃ¢ÂÂelectron atom with atomic number $Z$) one finds:
Electron speed
$$v_n=\frac{Ze^2}{2\varepsilon_0h}\,\frac1n\;\propto\;\frac1n$$
Energy
$$E_n=-\frac{m_eZ^2e^4}{8\varepsilon_0^2h^2}\,\frac1{n^2}\;\propto\;-\frac1{n^2}$$
Orbit radius
$$r_n=\frac{\varepsilon_0h^2}{\pi m_e e^2}\,n^2\;\propto\;n^2$$
So the dependencies $\bigl(v_n,\,E_n,\,r_n\bigr)$ go as
$\displaystyle\frac1n,\;\frac1{n^2},\;n^2$,
which corresponds to Option B.

Answer

$\frac{1}{n}, n^2, \frac{1}{n^2}$

Answer

$\frac{1}{n}, \frac{1}{n^2}, n^2$

Answer

$n, \frac{1}{n^2}, n^2$

Answer

$\frac{1}{n^2}, \frac{1}{n}, n^2$

Atoms & Nuclei

According to Bohr's theory of hydrogen atom, the speed of the electron, its energy and radius of its orbit vary with the principal quantum number n, respectively as

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