Question 407: Atoms & Nuclei

Question

The first three spectral lines of H-atom in the Balmer series are given $$\lambda$$1, $$\lambda$$2, $$\lambda$$3 considering the Bohr atomic model, the wave lengths of first and third spectral lines $$\left( \frac{\lambda_{1} }{\lambda_{3} } ight)   $$ are related by a factor of approximately 'x' $$	imes$$ 10$$-$$1.The value of x, to the nearest integer, is _________.

Accepted Answer

For 1
st
line
$${1 \over {{\lambda _1}}} = R{z^2}\left( {{1 \over {{2^2}}} - {1 \over {{3^2}}}} ight)$$
$${1 \over {{\lambda _1}}} = R{z^2}{5 \over {36}}$$ ..... (i)
For 3
rd
line
$${1 \over {{\lambda _3}}} = R{z^2}\left( {{1 \over {{2^2}}} - {1 \over {{5^2}}}} ight)$$
$${1 \over {{\lambda _3}}} = R{z^2}{{21} \over {100}}$$ ...... (ii)
Dividing (ii) by (i),
$${{{\lambda _1}} \over {{\lambda _3}}} = {{21} \over {100}} 	imes {{36} \over 5} = 1.512 = 15.12 	imes {10^{ - 1}}$$
$$x \approx 15$$

Atoms & Nuclei

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