atom. Find the wavelengths of the transitions from n₁ = 3 to n₂ = 2 for hydrogen
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- As per Bohr's model of atoms, electrons can move between states by absorbing or emitting radiation.
- When the electron moves to a higher state it will do so by absorbing energy in the form of a photon and when they are moving down to a lower level it will emit a photon.
- The wavelength of the photon is given by the Rydberg formula,
Here R∞ is the Rydberg constant and has a value of 1.097373 × 107 m-1, and n1 and n2 are the states in which transition takes place.
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- Normalize the wavefunction for the 2s orbital of a hydrogen electron. 3 Rn. 1 (r) = = (²/7) ² (2 − p) e - ² - a 2Zr na3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction is (2a.)3/2 /3a. 2ao , where a, is the Bohr radius. (a) 2-axis? What possible angles might the angular momentum vector L make with the (b) What is the most probable radius (in terms of a,) at which the electron is found? (c) What is the expectation value of r in this state? Note: xe-"dx = 120. (p) S° x*e-dx = 23.91. What is the probability of finding such an electron between a, and oo? Note:3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction e 2ao, where a, is the Bohr radius. 1 is (2ао)3/2 VЗа. (а) What possible angles might the angular momentum vector L make with the Z-axis? (b) What is the most probable radius (in terms of a.) at which the electron is found? (c) What is the expectation value of r in this state? Note: S xe-"dx 120. (d) What is the probability of finding such an electron between a, and ∞? Note: ° x*e-"dx = 23.91.