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Bohr's Model of an Atom

A single elec...

Question

A single electron orbits a stationary nucleus of charge $+ Z$ , where $Z$ is a constant. It requires 47.2 eV to excite electron from second Bohr orbit to third Bohr orbit, find the value of $Z$ .

A

1

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B

3

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C

5

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D

4

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Solution

The correct option is C 5
Position is $n_{1} = 2 \Rightarrow n_{2} = 3$ and $Δ E = 47.2 e V$
We have $Δ E = 13.6 z^{2} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}) e V$
$47.2 = 13.6 z^{2} (\frac{1}{2^{2}} - \frac{1}{3^{2}})$
$z = 5$

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