Spectral lines of hydrogen-like ions arise from electronic transitions between Bohr orbits

CHEMISTRY · Multi-part · CBSE · Chemistry · Structure of Atom · Structure of Atom

Problem

Spectral lines of hydrogen-like ions arise from electronic transitions between Bohr orbits. Consider the ions

C^{5+}

(Z = 6) and

He^{+}

(Z = 2). (a) Derive an expression for the difference in energy

\Delta E

between two arbitrary Bohr levels

n_{2}

(upper) and

n_{1}

(lower) of a hydrogen-like ion of atomic number

Z

. (b) Using your result from part (a), calculate the frequency of the photon emitted when an electron in

C^{5+}

jumps from

n = 4

n = 2

. (c) For the same transition (

n = 4 \rightarrow 2

) in

He^{+}

, determine the ratio of the frequencies of photons emitted by

C^{5+}

and

He^{+}