JEE MAIN - Physics (2021 - 16th March Morning Shift - No. 27)
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 $$\left( \frac{\lambda_{1} }{\lambda_{3} } \right) $$ are related by a factor of approximately 'x' $$\times$$ 10$$-$$1.
The value of x, to the nearest integer, is _________.
given $$\lambda$$1, $$\lambda$$2, $$\lambda$$3 considering the Bohr atomic model, the wave lengths of first and third spectral lines $$\left( \frac{\lambda_{1} }{\lambda_{3} } \right) $$ are related by a factor of approximately 'x' $$\times$$ 10$$-$$1.
The value of x, to the nearest integer, is _________.
Answer
15
Explanation
For 1st line
$${1 \over {{\lambda _1}}} = R{z^2}\left( {{1 \over {{2^2}}} - {1 \over {{3^2}}}} \right)$$
$${1 \over {{\lambda _1}}} = R{z^2}{5 \over {36}}$$ ..... (i)
For 3rd line
$${1 \over {{\lambda _3}}} = R{z^2}\left( {{1 \over {{2^2}}} - {1 \over {{5^2}}}} \right)$$
$${1 \over {{\lambda _3}}} = R{z^2}{{21} \over {100}}$$ ...... (ii)
Dividing (ii) by (i),
$${{{\lambda _1}} \over {{\lambda _3}}} = {{21} \over {100}} \times {{36} \over 5} = 1.512 = 15.12 \times {10^{ - 1}}$$
$$x \approx 15$$
$${1 \over {{\lambda _1}}} = R{z^2}\left( {{1 \over {{2^2}}} - {1 \over {{3^2}}}} \right)$$
$${1 \over {{\lambda _1}}} = R{z^2}{5 \over {36}}$$ ..... (i)
For 3rd line
$${1 \over {{\lambda _3}}} = R{z^2}\left( {{1 \over {{2^2}}} - {1 \over {{5^2}}}} \right)$$
$${1 \over {{\lambda _3}}} = R{z^2}{{21} \over {100}}$$ ...... (ii)
Dividing (ii) by (i),
$${{{\lambda _1}} \over {{\lambda _3}}} = {{21} \over {100}} \times {{36} \over 5} = 1.512 = 15.12 \times {10^{ - 1}}$$
$$x \approx 15$$
Comments (0)
