It requires 68eV of energy to excite the electron from the second Bohr orbit to the third Bohr orbit in a particular single electron species having a nuclear charge of +Ze , where Z is a constant and e is the magnitude of the electronic charge. Figure out the value of Z .

Question

It requires 68eV of energy to excite the electron from the second Bohr orbit to the third Bohr orbit in a particular single electron species having a nuclear charge of +Ze , where Z is a constant and e is the magnitude of the electronic charge. Figure out the value of Z . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

The energy required to excite the electron from second (n=2) Bohr orbit to the third (n=3) Bohr orbit is given by

Δ E = E_{3} - E_{2}

= (- \frac{Z ^{2} \times 13.6}{3 ^{2}}) - (- \frac{Z ^{2} \times 13.6}{2 ^{2}})

= z^{2} \times 13.6 (\frac{1}{4} - \frac{1}{9})

= Z^{2} \times 13.6 \times \frac{5}{36} \dots . (i)

But Δ E = E_{3} - E_{2} = 68 e V

From equations (i) and (ii),

∴ 68 e V = Z^{2} \times 13.6 \times \frac{5}{36} e V

∴ Z^{2} = \frac{36}{5} \times \frac{68}{13.6} = 36 \Rightarrow Z = 6

Q. It requires 68eV of energy to excite the electron from the second Bohr orbit to the third Bohr orbit in a particular single electron species having a nuclear charge of +Ze , where Z is a constant and e is the magnitude of the electronic charge. Figure out the value of Z .

Q. It requires $68 e V$ of energy to excite the electron from the second Bohr orbit to the third Bohr orbit in a particular single electron species having a nuclear charge of $+ Z e$ , where $Z$ is a constant and $e$ is the magnitude of the electronic charge. Figure out the value of $Z$ .