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The wavelength of the radiation emitted, when in hydrogen atom electron falls from infinity to stationary state 1, would be (Rydberg constant = 1.097×107 m-1)
- a)91 nm
- b)9.1 x 10-8 nm
- c)406 nm
- d)192 nm
Correct answer is option 'A'. Can you explain this answer?
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The wavelength of the radiation emitted, when in hydrogen atom electro...
Z=1 for the Hydrogen atom.
So,
So,
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The wavelength of the radiation emitted, when in hydrogen atom electro...
Explanation:
Bohr's Model:
- According to Bohr's model, when an electron falls from infinity to the stationary state 1 in a hydrogen atom, the wavelength of the radiation emitted can be calculated using the Rydberg formula.
- The Rydberg constant is given as 1.097 x 10^7 m^-1.
Calculating Wavelength:
- The formula to calculate the wavelength of the emitted radiation is given by: 1/λ = R(1/n1^2 - 1/n2^2)
- Here, n1 = 1 (initial state), n2 = ∞ (final state), R = Rydberg constant.
- Plugging in the values, we get: 1/λ = 1.097 x 10^7 (1/1 - 1/∞)
- As 1/∞ approaches 0, the equation simplifies to: 1/λ = 1.097 x 10^7
- Therefore, the wavelength of the radiation emitted when the electron falls from infinity to stationary state 1 in a hydrogen atom is 91 nm.
Final Answer:
- The correct answer is option 'A': 91 nm.
Bohr's Model:
- According to Bohr's model, when an electron falls from infinity to the stationary state 1 in a hydrogen atom, the wavelength of the radiation emitted can be calculated using the Rydberg formula.
- The Rydberg constant is given as 1.097 x 10^7 m^-1.
Calculating Wavelength:
- The formula to calculate the wavelength of the emitted radiation is given by: 1/λ = R(1/n1^2 - 1/n2^2)
- Here, n1 = 1 (initial state), n2 = ∞ (final state), R = Rydberg constant.
- Plugging in the values, we get: 1/λ = 1.097 x 10^7 (1/1 - 1/∞)
- As 1/∞ approaches 0, the equation simplifies to: 1/λ = 1.097 x 10^7
- Therefore, the wavelength of the radiation emitted when the electron falls from infinity to stationary state 1 in a hydrogen atom is 91 nm.
Final Answer:
- The correct answer is option 'A': 91 nm.
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The wavelength of the radiation emitted, when in hydrogen atom electron falls from infinity to stationary state 1, would be (Rydberg constant = 1.097×107 m-1)a)91 nmb)9.1 x 10-8 nmc)406 nmd)192 nmCorrect answer is option 'A'. Can you explain this answer?
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