If '$\lambda_1$' and '$\lambda_2$' are the wavelengths of the first member of the Balmer and Paschen series, in hydrogen atom respectively, then the ratio of respective frequencies, $f_1/f_2$ , is

Question

In an a.c. circuit, voltage and current are given by: \[ V = 100 \sin(100t) \, \text{V} \quad \text{and} \quad I = 100 \sin\left(100t + \frac{\pi}{3}\right) \, \text{mA}. \] The average power dissipated in one cycle is:

Answer 1

Step 1: Use energy
Photon energy is proportional to $\frac1{n_1^2}-\frac1{n_2^2}$, and the frequency is proportional to the energy.

Step 2: Values
Balmer: $\frac14-\frac19=\frac5{36}$. Paschen: $\frac19-\frac1{16}=\frac7{144}$.

Step 3: Divide
$\frac{5}{36}\div\frac{7}{144}=\frac{20}{7}$, the first option.

Final Answer:
The frequency ratio is $20:7$. \[ \boxed{\text{(A) }20:7} \]

If '\(\lambda_1\)' and '\(\lambda_2\)' are the wavelengths of the first member of the Balmer and Paschen series, in hydrogen atom respectively, then the ratio of respective frequencies, \(f_1/f_2\) , is

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The Correct Option is A

Solution and Explanation

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