In H-like species, an electron jumps from an orbital having two radial and two angular nodes to the orbital having same sign of wave function in all direction, at any distance. If energy of the emitte

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In H-like species, an electron jumps from an orbital having two radial and two angular nodes to the orbital having same sign of wave function in all direction, at any distance. If energy of the emitted photon is 326.4 eV , the species is:

TestHub · Accepted Answer

The final orbital has same sign of wave function, meaning it is a 1s orbital. Two radial and two angular nodes indicate a 4d orbital. Thus, the transition is 4d → 1s.

Energy is given by $13.6 Z^{2} (\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}}) e V$ .

$326.4 = 13.6 Z^{2} (\frac{1}{1 ^{2}} - \frac{1}{4 ^{2}}) = 13.6 Z^{2} (\frac{15}{16})$

$Z^{2} = \frac{326.4 \times 16}{13.6 \times 15} = 25.6 \approx 25$

$Z = 5$ . Hence, the species is B⁴⁺.

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