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The radius of an orbit of the electron, in a hydrogen like atom, is 4.5 a0 , where a0 is the Bohr’s radius for hydrogen. Its corresponding orbital angular momentum is 3h/2π . (h = Planck’s constant; R = Rydberg’s constant). The wave length, this atom would not be emitting, as it de–exites itself, is

(1) 9/32 R

(2) 9/16 R

(3) 9/5R

(4) 1/3R

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(2) 9/16 R

Since we are given that angular momentum = 3h/2π = n h/2π, hence n = 3

The radius, rn , of the nth allowed orbit, is given by rn ∝ n2/z

The wavelength, λ, of the emitted radiation, is

The three different ways, the atom can de–excute itself (from the state with n = 3) are

(i) n2 = 3 → n1 = 1; (ii) n2 = 3 → n1 = 2; and (iii) n2 = 2 → n1 = 1.

The corresponding wavelengths are

It follows that, out of the given values λ = 9/16 R, is the value , that the atom would not emit.

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