MCQ
The masses of photons corresponding to the first lines of Lyman and Balmer series of the spectrum of hydrogen atom are in the ratio of
- ✓$27 : 5$
- B$3 : 2$
- C$2 : 3$
- D$4 : 9$
✓
Answer
Correct option: A.
$27 : 5$
a
since energy is directly proportional to mass and mass is inversely proportional to wavelength ( $\lambda=\frac{h}{m v}$ Deleroglie's wavelength Equation)
since energy is directly proportional to mass and mass is inversely proportional to wavelength ( $\lambda=\frac{h}{m v}$ Deleroglie's wavelength Equation)
Lyman Series: $\frac{1}{\lambda_{1}}=R_{H}\left(1-\frac{1}{4}\right)=\frac{3 R_{H}}{4}$ where $R_{H}$ =Rydberg Constant
Balmer Series: $\frac{1}{\lambda_{2}}=R_{H}\left(\frac{1}{4}-\frac{1}{9}\right)=\frac{5 R_{H}}{36}$
$\lambda_{1}: \lambda_{2}=\frac{5 R_{H}}{36} \times \frac{4 R_{H}}{3}=\frac{5}{27}$
$m_{1}: m_{2}=27: 5$
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