Question

For wavelength of visible radiation of Hydrogen spectrum, Balmer gave an equation as \(λ = \frac{xm^2}{m^2-4}\), where m is the integer value. The value of x in terms of Rydberg's constant R is

• A. \(\frac{R}{4}\)
• B. \(\frac{4}{R}\)
• C. \(2R\)
• D. \(4R\)

Hint:

Start from \(\dfrac1\lambda=R\left(\dfrac1{2^2}-\dfrac1{m^2}\right)\) and invert.

Answer 1

The Correct Option is B

Step 1: Check by a limit
As $m\to\infty$, $\lambda\to x$, which is the series limit. The Balmer limit is $\dfrac1\lambda=\dfrac R4$.

Step 2: Read off
So $x=\dfrac4R$, option (B).

Final Answer:
$x=4/R$, option (B). \[ \boxed{\dfrac4R} \]