Calculate the wavelength for the emission transition if it starts from the orbit having radius $1.3225$ nm and ends at the one having $211.6$ pm. Name the series to which this transition belongs and the region of the spectrum.

Open in App

Solution

The radius of $n$ th orbit of H-like species is given by the expression $\frac{0.529 n^{2}}{Z} ˚ A$ or $\frac{52.9 n^{2}}{Z}$ pm.
$r_{1} = 1.3225$ nm $= 1322.5$ pm $= \frac{52.9 n_{1}^{2}}{Z}$ pm $. . . . . . (1)$
$r_{2} = 211.6$ pm $= \frac{52.9 n_{2}^{2}}{Z}$ pm $. . . . . . (2)$
Dividing $(1)$ by $(2)$ , we get
$\frac{r_{1}}{r_{2}} = \frac{1322.5}{211.6} = \frac{n_{1}^{2}}{n_{2}^{2}}$
$\frac{n_{1}^{2}}{n_{2}^{2}} = 6.25$ $⟹ \frac{n_{1}}{n_{2}} = 2.5$
$n_{2} = 5$ , $n_{1} = 2$ .
The transition is in Balmer series.
$¯ ν = 1.097 \times 10^{7} (\frac{1}{2^{2}} - \frac{1}{5^{2}}) = 1.097 \times 10^{7} \times 0.21 m^{- 1}$
$λ = \frac{1}{v} = \frac{1}{23.037 \times 10^{5}} = 434 \times 10^{- 9}$ m or $434$ nm
The transition lies in the visible region.

Suggest Corrections

Similar questions

Calculate the wavelength for the emission transition if it starts from the orbit having radius 1.3225 nm and ends at 211.6 pm. Name the series to which this transition belongs and the region of the spectrum.

Q. What would be the wavelength and name of series respectively for the emission transition for H-atom if it starts from the orbit having radius 1.3225 nm and ends at 211.6 pm?

Q. Emission transitions in the Paschen series end at orbit

n

=

3

and start from orbit

n

and can be represented as

v = 3.29 \times 10^{15} (H z) [1 / 3^{2} - 1 / n^{2}]

Calculate the value of

n

if the transition is observed at 1.285 nm. Find the region of the spectrum.

Q. Emission transitions in the Paschen series end at orbit n = 3 and start from orbit n and can be represented as

v = 3.29 \times 10^{15} (H z) [1 / 3^{2} - 1 / n^{2}]

.
Calculate the value of n if the transition is observed at 1285 nm. Find the region of the spectrum.

Emission transitions in the Paschen series end at orbit n = 3 and start from orbit n and can be represented as v = 3.29 × $10^{1} 5$ (Hz) [1/ $3^{2}$ – 1/ $n^{2}$ ] Calculate the value of n if the transition is observed at 1285 nm. Find the region of the spectrum.

Join BYJU'S Learning Program

Calculate the wavelength for the emission transition if it starts from the orbit having radius 1.3225 nm and ends at the one having 211.6 pm. Name the series to which this transition belongs and the region of the spectrum.

Calculate the wavelength for the emission transition if it starts from the orbit having radius $1.3225$ nm and ends at the one having $211.6$ pm. Name the series to which this transition belongs and the region of the spectrum.