Question 650: Atoms & Nuclei

Question

The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is

Accepted Answer

For largest $$\lambda$$ in UV $$	o$$ 122 nm
For $$\Delta$$E$$_{\mathrm{min}}$$,
$${1 \over {{\lambda _{lyman}}}} = {R_c}\left( {1 - {1 \over 4}} ight)$$
[$$\because$$ $${1 \over \lambda } = {R_c}\left( {{1 \over {n_2^2}} - {1 \over {n_1^2}}} ight)$$]
$${1 \over {{\lambda _{lyman}}}} = {{3{R_c}} \over 4}$$ ..... (i)
R$$_c$$ = Rydber constant = 1.097 $$	imes$$ 10$$^7$$ m$$^{-1}$$
For min $$\lambda$$ in IR region, n = D $$	o$$ n = 3
$${1 \over {{\lambda _{IR}}}} = {{{R_c}} \over 9}$$ ...... (ii)
On dividing eq. (i) by (ii)
$${1 \over {{\lambda _{lyman}}}} 	imes {\lambda _{IR}} = {1 \over {{{3{R_c}} \over 4}}} 	imes {9 \over {{R_c}}} = {{3{R_c}} \over 4} 	imes {9 \over {{R_c}}} = {{27} \over 4}$$
$$	herefore$$ $${\lambda _{IR}} = {{27} \over 4} 	imes 122$$ nm = 823.5 nm

Answer

802 nm

Answer

823 nm

Answer

1882 nm

Answer

1648 nm

Atoms & Nuclei

The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is

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