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the energy corresponding to one the line in paschen series for h- atom is 18.1652×10^-20 J.find the quantum no n2 for the transition which produces this line.
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the energy corresponding to one the line in paschen series for h- atom...
Energy Calculation for Paschen Series Line:
- The energy of a spectral line in the Paschen series can be calculated using the formula:
E = -2.179 × 10^-18 J (Z^2 / n^2)
Given Energy:
- Energy = 18.1652 × 10^-20 J
Finding Quantum Number n2:
- Substitute the given energy into the formula:
18.1652 × 10^-20 = -2.179 × 10^-18 (1^2 / n2^2)
- Solve for n2:
n2^2 = 1 / (18.1652 / 2.179)
n2^2 = 1 / 8.345
n2^2 = 0.1196
n2 = √0.1196
n2 ≈ 0.346
Explanation:
- The quantum number n2 represents the energy level to which the electron transitions in the hydrogen atom to produce the spectral line.
- In this case, the transition corresponding to the given energy of 18.1652 × 10^-20 J occurs from the n=2 energy level to the n=0.346 energy level.
- The transition produces a spectral line in the Paschen series for hydrogen atom.
Conclusion:
- The quantum number n2 for the transition which produces the given Paschen series line energy is approximately 0.346.
- The energy of a spectral line in the Paschen series can be calculated using the formula:
E = -2.179 × 10^-18 J (Z^2 / n^2)
Given Energy:
- Energy = 18.1652 × 10^-20 J
Finding Quantum Number n2:
- Substitute the given energy into the formula:
18.1652 × 10^-20 = -2.179 × 10^-18 (1^2 / n2^2)
- Solve for n2:
n2^2 = 1 / (18.1652 / 2.179)
n2^2 = 1 / 8.345
n2^2 = 0.1196
n2 = √0.1196
n2 ≈ 0.346
Explanation:
- The quantum number n2 represents the energy level to which the electron transitions in the hydrogen atom to produce the spectral line.
- In this case, the transition corresponding to the given energy of 18.1652 × 10^-20 J occurs from the n=2 energy level to the n=0.346 energy level.
- The transition produces a spectral line in the Paschen series for hydrogen atom.
Conclusion:
- The quantum number n2 for the transition which produces the given Paschen series line energy is approximately 0.346.
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the energy corresponding to one the line in paschen series for h- atom is 18.1652×10^-20 J.find the quantum no n2 for the transition which produces this line.
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