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Bohr's Model of Atom

Number of rev...

Question

Number of revolution per second made by electron in Bohr orbit is called orbital frequency. If $u_{n}, r_{n}, E_{n}$ are velocity, radius and energy level of $n$ th orbit respectively?

\frac{u_{n}}{2 π r_{n}}

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- \frac{2 E_{n}}{n h}

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- \frac{2 E_{1}}{n^{3} h}

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either of these

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Solution

The correct option is C either of these
According to Bohr model,
$u_{n} = \frac{2 π e^{2}}{n h}$

$r_{n} = \frac{n^{2} h^{2}}{4 π^{2} m e^{2}}$
and
$E_{n} = - \frac{2 π^{2} m e^{4}}{n^{2} h^{2}}$

Orbital frequency is the number of orbits a certain object makes around another object in unit second.

$∴$ orbital frequency $= \frac{u_{n}}{2 π r_{n}}$
(by putting value of u and r.)

$= \frac{2 π e^{2} \times 4 π^{2} m e^{2}}{n h \times 2 π \times n^{2} h^{2}}$

(by putting value of $E_{n}$ )

$= - \frac{2 E_{n}}{n h}$
$[E_{n} = - \frac{2 π^{2} m e^{4}}{n^{2} h^{2}}]$

(by putting value of $E_{1}$ )

$= - \frac{2 E_{1}}{n h \times n^{2}} = - \frac{2 E_{1}}{n^{3} h}$

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Number of revolution per second made by electron in Bohr orbit is called orbital frequency. If un,rn,En are velocity, radius and energy level of nth orbit respectively?

Number of revolution per second made by electron in Bohr orbit is called orbital frequency. If $u_{n}, r_{n}, E_{n}$ are velocity, radius and energy level of $n$ th orbit respectively?