The radius of the orbit of an electron in a Hydrogen-like atom is 4.5 a0, where a0 is the Bohr radius. Its orbital angular momentum is \frac{3 h}{2 \pi} . It is given that h is Planck constant and R is Rydberg constant. The possible wavelength (s), when the atom de-excites, is (are)

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The radius of the orbit of an electron in a Hydrogen-like atom is 4.5 a₀, where a₀ is the Bohr radius. Its orbital angular momentum is $\frac{3 h}{2 π}$ . It is given that h is Planck constant and R is Rydberg constant. The possible wavelength (s), when the atom de-excites, is (are)

$\frac{9}{16 R}$

$\frac{9}{5 R}$

$\frac{9}{32 R}$

$\frac{9}{3 R}$

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$4 .5 g = \frac{n^{2} a_{0}}{z}$

$4 .5 = \frac{9}{z} \Rightarrow z = 2$

$\frac{1}{λ} = 4 R (\frac{1}{1^{2}} - \frac{1}{3^{2}}) \Rightarrow λ = \frac{9}{32 R}$

$\frac{1}{λ} = 4 R (\frac{1}{2^{2}} - \frac{1}{3^{2}}) \Rightarrow λ = \frac{9}{5 R}$

$\frac{1}{λ} = 4 R (\frac{1}{1^{2}} - \frac{1}{2^{2}}) \Rightarrow λ = \frac{3}{R}$

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