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Assertion: In a hydrogen atom energy of ...

Assertion: In a hydrogen atom energy of emitted photon corresponding to transition from `n = 2` to `n = 1` is such greater as compared to transition from `n=oo` to `n = 2`.
Reason: Wavelength of photon is directly proportional to the energy of emitted photon.

A

Statement I is True , Statement II is True , Statement II is a correct explanation for Statement I.

B

Statement I is True , Statement II is True , Statement II is NOT a correct explanation for Statement I.

C

Statement I is True , Statement II is False.

D

Statement I is False , Statement II is True.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that the energy of the emitted photon corresponding to the transition from \( n = 2 \) to \( n = 1 \) is greater than the energy of the emitted photon corresponding to the transition from \( n = \infty \) to \( n = 2 \). 2. **Calculating Energy for Transition from \( n = 2 \) to \( n = 1 \)**: - The formula for the energy of the emitted photon during a transition in a hydrogen atom is given by: \[ E = -13.6 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \] - For the transition from \( n = 2 \) to \( n = 1 \): \[ E_{2 \to 1} = -13.6 \left( \frac{1}{1^2} - \frac{1}{2^2} \right) = -13.6 \left( 1 - \frac{1}{4} \right) = -13.6 \left( \frac{3}{4} \right) = -10.2 \text{ eV} \] 3. **Calculating Energy for Transition from \( n = \infty \) to \( n = 2 \)**: - For the transition from \( n = \infty \) to \( n = 2 \): \[ E_{\infty \to 2} = -13.6 \left( \frac{1}{\infty^2} - \frac{1}{2^2} \right) = -13.6 \left( 0 - \frac{1}{4} \right) = 13.6 \times \frac{1}{4} = 3.4 \text{ eV} \] 4. **Comparing Energies**: - Now we compare the two energies: - \( E_{2 \to 1} = 10.2 \text{ eV} \) - \( E_{\infty \to 2} = 3.4 \text{ eV} \) - Since \( 10.2 \text{ eV} > 3.4 \text{ eV} \), the assertion is **correct**. 5. **Understanding the Reason**: - The reason states that the wavelength of the photon is directly proportional to the energy of the emitted photon. - However, we know that the relationship between energy (E) and wavelength (λ) is given by: \[ E = \frac{hc}{\lambda} \] - From this, we can derive that: \[ \lambda = \frac{hc}{E} \] - This shows that wavelength is **inversely** proportional to energy, not directly proportional. Therefore, the reason is **incorrect**. 6. **Conclusion**: - The assertion is true, but the reason is false. Thus, the correct option is that the assertion is true and the reason is false. ### Final Answer: The correct option is **C**: Assertion is true, Reason is false.

To solve the question, we need to analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that the energy of the emitted photon corresponding to the transition from \( n = 2 \) to \( n = 1 \) is greater than the energy of the emitted photon corresponding to the transition from \( n = \infty \) to \( n = 2 \). 2. **Calculating Energy for Transition from \( n = 2 \) to \( n = 1 \)**: ...
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