Question

In Hydrogen emission spectrum electron transition takes place from $\mathrm{n}=8$ to $\mathrm{n}={\mathrm{n}}_{\mathrm{f}}$. If we plot this graph of $\overline{\mathrm{v}}$ vs $(1/{n_f}^2)$. Which of the following statement is correct?

• A. Slope = $-{\mathrm{R}}_{\mathrm{H}}$
• B. Slope = ${\mathrm{R}}_{\mathrm{H}}$
• C. Intercept = ${\mathrm{R}}_{\mathrm{H}}$
• D. Graph is non-linear

Answer 1

The correct option is B

Slope = ${\mathrm{R}}_{\mathrm{H}}$

Step 1:the transition state is $\mathrm{n}=8$ to $n=n_f$

so, ${\mathrm{n}}_1=8$ and$n_2=n_f$………(A)

According to the Rydberg equation$\frac{1}{\lambda }=R_H{z}^2\left[\left(\frac{1}{{n_1}^2}\right)–\left(\frac{1}{{n_2}^2}\right)\right]$ (Z = 1 for hydrogen emission spectrum) ………(B)

Step 2: Put equation (A) in equation (B),

Thus, $\frac{1}{\lambda }=R_H{1}^2\left[\left(\frac{1}{8^2}\right)–\left(\frac{1}{{n_f}^2}\right)\right]$………… (1)

Also, $y=m{c}^2$………… (2)

Comparing (1) and (2), we get

$m=R_H$or $slope=R_H$

Final Answer: The correct answer is option B.