Question

For emission line of atomic hydrogen from ni=8 to nf- the plot of wavenumber (v) against (1/n2) will be:(The Rydberg constant, RH is in wave number unit).

• A. Non-linear
• B. Linear with slope ${\mathrm{R}}_{\mathrm{H}}$
• C. Linear with slope – ${\mathrm{R}}_{\mathrm{H}}$
• D. Linear with intercept- ${\mathrm{R}}_{\mathrm{H}}$

Answer 1

The correct option is B

Linear with slope ${\mathrm{R}}_{\mathrm{H}}$

An explanation for correct option:

Option (B): Linear with slope ${\mathrm{R}}_{\mathrm{H}}$

• For this we can use Rydberg Formula as;

⇒ $$\begin{gathered} \frac{1}{\mathrm{\lambda }}=\stackrel{-}{v}={\mathrm{R}}_H{Z}^2\left(\frac{1}{n_1^2}-\frac{1}{n^2}\right) \\ \stackrel{-}{v}={\mathrm{R}}_H{Z}^2\left(\frac{1}{n_1^2}-\frac{1}{8^2}\right) \\ \mathit{}\mathit{}\mathit{}\therefore \mathit{}\stackrel{\mathit{-}}{v}={\mathrm{R}}_H\mathit{\times }\frac{\mathit{1}}{n_{\mathit{1}}^{\mathit{2}}}\mathit{-}\frac{R_H}{\mathit{64}} \end{gathered}$$ (The Rydberg constant, R_H is in wave number unit).

• The equation of the line follows ,$\mathrm{y}=\mathrm{mx}+\mathrm{c}$,
• Hence, the slope here is ${\mathrm{R}}_{\mathrm{H}}$(Rydberg constant).

An explanation for the incorrect option:

Option (A): Non-linear

• As we have seen the equation given above follows the equation of the straight line,$\mathrm{y}=\mathrm{mx}+\mathrm{c}$.
• So, option A stating the equation to be nonlinear is an incorrect option.

Option (C): Linear with slope – ${\mathrm{R}}_{\mathrm{H}}$

• The slope of the equation turned out to be ${\mathrm{R}}_{\mathrm{H}}$(Rydberg constant).
• It has a positive slope with a linear equation.
• But, the option given as Linear with slope $–{\mathrm{R}}_{\mathrm{H}}$ (negative slope) is not correct.

Option (D): Linear with intercept- ${\mathrm{R}}_{\mathrm{H}}$

• Here the slope, that has been found for the linear equation is ${\mathrm{R}}_{\mathrm{H}}$(Rydberg constant).
• Here in the equation, the intercept is the origin itself.
• But, the option is given as Linear with intercept to be ${\mathrm{R}}_{\mathrm{H}}$ is not correct.

Hence, For the emission line of atomic hydrogen from ni=8 to nf- the plot of wavenumber (v) against (1/n2) will be Linear with slope${\mathrm{R}}_{\mathrm{H}}$ Option (B).