Atomic StructureMedium

Question

Which of the following statement(s) is/are correct?

Options

A.The ratio of the radii of the first three Bohr orbits of hydrogen atom is 1: 8: 27.
B.The ratio of magnitude of total energy: kinetic energy: potential energy for electron in any orbit of hydrogen atom is 1: 1: 2.
C.The frequency of a green light is 6 × 1014 Hz, then its wavelength is 500 nm.
D.The ratio of de Broglie wavelength of a H-atom, He-atom and CH4-molecule moving with equal kinetic energy is 4: 2: 1.

Solution

$(a)r_{1}:r_{2}:r_{3} = 1^{2}:2^{2}:3^{2} = 1:4:9$

$(c)\lambda = \frac{c}{v} = \frac{3 \times 10^{8}}{6 \times 10^{14}} = 5 \times 10^{- 7}\text{ m = 500 nm}$

$(d)\lambda = \frac{h}{\sqrt{2mE}} \Rightarrow \lambda \propto \frac{1}{\sqrt{m}} $$$\therefore\lambda_{H}:\lambda_{H_{e}}:\lambda_{cn_{4}} = \frac{1}{\sqrt{1}}:\frac{1}{\sqrt{4}}:\frac{1}{\sqrt{16}} = 4:2:1$$

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