Question

The energy (in joules) emitted when electrons of $1.0g$ atom of hydrogen undergo transition giving the spectral line of lowest energy in the visible region of its atomic spectrum is $x\times {10}^{4}J$
$(R_H=1.1\times {10}^7{m}^{-1};c=3\times {10}^{8}m{s}^{-1};h=6.6\times {10}^{-34}J-s);N_A=6\times {10}^{23}$ (Report your answer upto two decimal only)

Answer 1

The transition occurs like Balmer series as spectral line is observed in visible region.
Thus, the line of lowest energy will be observed when transition occurs from $3^{rd}$ orbit to $2^{nd}$ orbit, i.e., $n_1=2$ and $n_2=3$
$\frac{1}{\lambda }=R[\frac{1}{2^2}-\frac{1}{3^2}]=\frac{5}{36}RE=hv=h.\frac{c}{\lambda }=6.6\times {10}^{-34}\times 3\times {10}^8\times \frac{5}{36}\times 1.1\times {10}^7=3.025\times {10}^{-19}Jperatom$
Energy corresponding to $1.0g$ atom of hydrogen
$=3.025\times {10}^{-19}\times$ Avogadro's number
$=3.025\times {10}^{-19}\times 6\times {10}^{23}$J
$=18.15\times {10}^{4}J$
Hence, $x=18.15$