Question

Calculate the ratio of energies of 2nd orbits of H, He⁺ and Li⁺².

• A. 1:4:9
• B. 2:4:9
• C. 3:6:9
• D. 4:8:9

Answer 1

The correct option is A

1:4:9

The explanation for the correct answer:-

Given Data:

We have to find the ratios of energies of the 2nd orbit of $\mathrm{H},{\mathrm{He}}^{+},{\mathrm{Li}}^{2+}$

Also, the number of orbits (n) = 2.

Apply energy formula for single-electron species:

We know that energy of hydrogen-like species = $-13.6\frac{{\mathrm{z}}^2}{{\mathrm{n}}^2}\mathrm{eV}$

Now, As n= 2 (n = number of orbits) for all species given and -13.6 is also constant for $\mathrm{H},{\mathrm{He}}^{+},{\mathrm{Li}}^{2+}$

So, $\mathrm{E}\mathrm{\alpha }{\mathrm{Z}}^2$ ( $\mathrm{Z}$ = Atomic number)

The ratio of energies of $\mathrm{H},{\mathrm{He}}^{+},{\mathrm{Li}}^{2+}$ is $1^2:2^2:\hspace{0.17em}{3}^2$

Therefore the ratio of energies of $\mathrm{H},{\mathrm{He}}^{+},{\mathrm{Li}}^{2+}$ = $1:4:9$, option (A) is the correct answer.