Question

Calculate the ionization energy of hydrogen atom using Bohr’s theory.

Answer 1

Answer on Question #76516, Chemistry / Inorganic Chemistry

Calculate the ionization energy of hydrogen atom using Bohr's theory.

Solution

To answer this question we should use the equation:

$$E = h v = \frac{h c}{\lambda}$$

To find $\frac{1}{\lambda}$ we should use the Rydberg equation:

$$\frac{1}{\lambda} = R_{\infty} \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right)$$

Where $R_{\infty} = 1.09737316 \times 10^{7} \, \text{m}^{-1}$,

for hydrogen atom $n_f = 1, n_i = \infty$, then

$$\frac{1}{\lambda} = R_{\infty}$$

and

$$E = h v = \frac{h c}{\lambda} = h v R_{\infty}$$ $$E_i = 6.626 \times 10^{-34} \times 2.997 \times 10^{8} \times 1.09737316 \times 10^{7} = 2.179 \times 10^{-18} \, (\text{J})$$

Answer: $2.179 \times 10^{-18} \, (\text{J})$