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2. structure of atom — Chemistry STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceChemistry2. structure of atom1 Mark
MCQ
For emission line of atomic hydrogen from $n_1= 8$ to $n_f = n$, the plot of wave number $\left( {\bar v} \right)$ against $\left( {\frac{1}{{{n^2}}}} \right)$ will be(The Rydberg constant, $R_H$ is in wave number unit)
  • A
    Linear with intercept $- R_H$
  • B
    Non linear
  • C
    Linear with slope $R_H$
  • ✓
    Linear with slope $-R_H$
✓

Answer

Correct option: D.
Linear with slope $-R_H$
d
For emission line $n_f < n_i$

$\therefore \,\bar v = R{Z^2}\left[ {\frac{1}{{n_i^2}} - \frac{1}{{n_f^2}}} \right] = R\left[ {\frac{1}{{{8^2}}} - \frac{1}{{{n^2}}}} \right]$

or, $\bar v = {R_H}\left( {\frac{1}{{64}} - \frac{1}{{{n^2}}}} \right)$

$ = \frac{{{R_H}}}{{64}} - \frac{{{R_H}}}{{{n^2}}}$

$\bar v =  - {R_H}\left( {\frac{1}{n^2}} \right) + \frac{{{R_H}}}{{64}}$

$\therefore \,y = mx + c$

Slope $= -R_H$ 

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