The hydrogen-like atom has one electron revolving around a stationary nucleus. The energy required to execute electron from the second orbit to the third orbit is 42.7eV. The atomic number of the atom is _______?

The hydrogen-like atom has one electron revolving around a stationary nucleus. The energy required to execute electron from the second orbit to the third orbit is 42.7eV. The atomic number of the atom is _______?

Explanation

The energy required to excite an electron from the second orbit to the third orbit is:

ΔE = 13.6Z^2(1/4 - 1/9) eV

Given ΔE = 42.7 eV:

42.7 = 13.6Z^2(1/4 - 1/9)

Solving for Z:

Z = 4