The electron in the n$$^{th}$$ orbit of Li$$^{2+}$$ is excited to (n+1) orbit using the radiation of energy $$1.47 \times 10^{-17}$$ J (as shown in the diagram). The value of n is _______ Given: $$R_H = 2.18 \times 10^{-18}$$ J

For Li²⁺ (Z=3), energy levels: $$E_n = -R_H \frac{Z^2}{n^2} = -\frac{9R_H}{n^2}$$

Energy for transition n → n+1:

$$\Delta E = 9R_H\left(\frac{1}{n^2} - \frac{1}{(n+1)^2}\right) = 1.47 \times 10^{-17}$$

$$\frac{1}{n^2} - \frac{1}{(n+1)^2} = \frac{1.47 \times 10^{-17}}{9 \times 2.18 \times 10^{-18}} = \frac{1.47}{1.962} = 0.75$$

Try n=1: $$1 - 1/4 = 0.75$$ ✓

The value of n is 1.